bn/tests/serialization.rs

extern crate rand;
extern crate bn;
extern crate bincode;
extern crate rustc_serialize;

use bn::*;

use bincode::SizeLimit::Infinite;
use bincode::rustc_serialize::{encode, decode};
use rustc_serialize::{Encodable, Decodable};
use rustc_serialize::hex::{FromHex, ToHex};

pub fn into_hex<S: Encodable>(obj: S) -> Option<String> {
    encode(&obj, Infinite).ok().map(|e| e.to_hex())
}

pub fn from_hex<S: Decodable>(s: &str) -> Option<S> {
    let s = s.from_hex().unwrap();

    decode(&s).ok()
}

pub fn reserialize<S: Encodable + Decodable>(obj: S) -> S {
    let s = into_hex(obj).unwrap();

    from_hex(&s).unwrap()
}

#[test]
fn group_serialization_and_deserialization() {
    let b = Fr::random(&mut rand::thread_rng());

    let mut a = G1::one();
    for _ in 0..100 {
        a = a * b;

        assert!(reserialize(a) == a);
        assert!(reserialize(reserialize(a)) == a);
        let mut c = a;
        c.normalize();

        assert!(a == c);
    }

    let mut a = G2::one();
    for _ in 0..100 {
        a = a * b;

        assert!(reserialize(a) == a);
        assert!(reserialize(reserialize(a)) == a);
        let mut c = a;
        c.normalize();

        assert!(a == c);

    }
}

#[test]
fn group_serialization_edge_cases() {
    assert!(from_hex::<G1>("00").unwrap() == G1::zero());
    assert!(from_hex::<G2>("00").unwrap() == G2::zero());
    assert!(from_hex::<G1>("23").is_none());
    assert!(from_hex::<G2>("23").is_none());

    // not points on the curve
    assert!(from_hex::<G1>("04177cedb64589bde7a64ad24f89bbb8c9f05535810865aaea8fbf8184ff9e120313500226b2422d2068614d1c8c7146c806a97743e78d9901748a9ded08ea9e5f").is_none());
    assert!(from_hex::<G2>("0404d4bf3239f77cee7b47c7245e9280b3e9c1182d6381a87bbf81f9f2a6254b731df569cda95e060bee91ba69b3f2d103658a7aea6b10e5bdc761e5715e7ee4bb01b4c328f0cbdb4aada63b3d09100d792376b94d07a6004e46054eeec849e8de9835158a11d28483dd8db236ea49f3630edc9e41944e494c5aacfc36af3b66e7").is_none());

    // out of bounds
    assert!(from_hex::<G2>("04ffd6a64a62b843a22c6250eda2354d603e74c30ed0b1435951c3f7dd541538beb8a43915823125c6bb89aece89125664ce78ca69b81cdb8164b40eb2833560b606e11258ce33c4076eff0d5824f210466b588d324b60ccd5a2b7f180f9a7cd7f1ab564ddb03b1b684ff4315acc6eef5229d99fe107afaea83a5c72f2b4c33aca").is_none());
}

#[test]
fn g1_vectors() {
    let expected = vec![
        "0400000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000002",
        "040e97c669de7c670d734ca98a3bc5176c8f82aa5e44f9a8780998c22dfa5fb5ea19305ad020d76d8529f57dbdc43f7e77a637f17b2d5db5b06a2554c1151b1255",
        "04070eef7bbfe7c9fa76338ed6d6a12b84f61a1a1b5b4d54c009b3993e2262c5fb1f4118919fac6678cb671ccfe5a3ab7ffc42dae56e8f4382ea3e6582ea7fdd15",
        "041ce66de558c33edf36b637bd39478e2f317f674e0559025d1e428f37dda84c342e916be0e1e8ab1ba6a9ef642a2f1de44c1f6f91aca23991cb636dbb997cbc01",
        "042e8d7e2ab119b53b2e2e5f8ddda2116aa821949ae0bd00a6ee6ebbe130397c0709e07974bfeae5c973c098c6dff65e864ee6ee05e9ccd1d61c8ca72e0c49232a",
        "040460253e7e4e9804bdc30e1d76f98d7f7fcb4a6845fd6f9df0f06a18e1a2ebb3066fddd38227281acd80b6b6253f5d89e401918586254edad1a56fbb8544dbbd",
        "04130f5f5f20846ffcd6dbfded402bebb7bb07e0a4cb2024bc84262de67498dd7e18dfc445b80fd0a1843d6ddb5ffc16cb8872c373b7adb9fd1b98ccc922318966",
        "042849878760819716f11108e902836a72f4bba88eadbe26b5b9f53e75c1f8714f0732eeeaacbbde8dce07be752d413d58538fc11f82a1c434afac5c27760e8688",
        "041846eb3215c26d8be94d8cb688f19f59db6c771bc8155d1fff826440bdaf8ce720553790d70aeccfb178e6c33f4331b8cc24e02c8ae8b5a0bb9b57a9c1132001",
        "0421f8b0a60f933351788799a7271fce8eb3349b98b1e0dae6a1de4eebba06daed2f966958654ace4bad972296bfd8d3f1568954bec25b665c0fc8f64f1a0c9856",
        "04163ddafd9f4677caa2b8feb510a6b0ef09191a00adfd9f09ae3e59d687af8ccb1a47d8362079b22c9064718f02948da7832a8e123b8c6e3730a9e7e137f84da7",
        "041ac98fe325a2faf01816da51b3733edb8a13935dc0b82a6fc2667773d09461ce258861533cd79b9ca801a366e40dbf61431296ca6431b51e61adb41e389328ea",
        "040dfcd832e70b1ebfc5f07d66ef71e88f1903eb69e25a43e17fcb119305f936a101f6022efdd7bb49bb2f9882d1edb54a618117ac9a213776ee09661dc813cb90",
        "041c11d08dd28ed037fb7800988bf9ed0ffe5dea2ee321ba36725bbc2fbda12df82151ba8776a883a4d2fdb5daefb681aed75636db330956b36a795031b238494a",
        "0407592e35e3444f61a5cd4bd3b62765ab5d67ff57b88aa781bfc0a14017746f9f2ff61c2caf223a33ea998503491389ec7b5ef2797f9d7bf5b63640cff086bc11",
        "040a5e52f3b28b3d8a4eae2332ddcfaeb3300432f9c11409c4388607dfe2a0dd171781fd5e8fffab898a916ee4436f487b7ff9a0a7ffdae2e0f98d6fc1075f60fe",
        "042db55c23fcdffc4000befcc40b612d1bc38d8e34ba4c1eb68f7a1446f851630d200c8cc5cf724a332ac366160836f91c086df5c8e023e0131eac51f1c18431c3",
        "04283f5279f2bc83c2c0829d1814f066d1828c267c95edc39ad4853c5cb35c02dd1f0f1bfd04a340863a34d8638c0b7c254473da29ec0c0a95fae6a7ccde78c740",
        "0401cf54e2dd9c2c97a96b809781114b82aee7d0b9f648d91fe01533062f99fe590037123d18acef099417572bdb041f77ef044b9c3fbef0ef0f9894f9a4061313",
        "040b0115940193b2c17fb561c317ed88d5b5bac173f4eacd887fc8de03b9915ce62be17e169ae45579e2f0982b686a611309a8435d1e2f0de9a49c97f72679c795",
        "04194e71fb26deed74c5681a0e616ed67135add9f3eb97fba96202539876fe0a642b27a2f7a125e849eca00af763e532d5c86ab650bcded04d47d26d8c6c62c139",
        "04001082425143d275f44e16040d7f8922ccdcd77892cd80796a86051f4ff5b2de272e4a7dbfccbd7ef79cae19d0de3a0697adc6cc44d99f014187a99b6c26d7cc",
        "041e6b87d81c1af93bacf529258f36145b434b84e843e0963674c529133b7ccbdc09384b95b6c343d8012f4a8b3a1bd6f34142d7688963df85c38369638b1c3117",
        "041e34c8d7c0ba039b67537c75939a14fd61598babc9a448cd103601253b93692c1eb61a4444ac063eb1ae75e77df30f69cda5dadc08912727ce2426276fca10ad",
        "041cd5b925c2174a380cf78f14a57388711b91c90010c55c0bea173cf77443869f1f7fdb3f0414e61d12589a46d8ae49f95ef9b1bece46a85d2d14d2deed1cbdaa",
        "042826a17e76e78d1883003a32e8cabf44ea62087a2ec95ef68d72ed31f0dc0eab11d1fcb397c18539c7ed620a502fba6f4ee19adc17aaf9501b801e72a21c7b9d",
        "0425b7a1770cc9e63055969af6b201dc7b6b5c8ac819b6ef82f39d3dec427a41c914b4f4c56c3fd44b34430f2a5cb7ae272c1a6fbcd86a22255db728fcc91d14b3",
        "04150f39cb53bcf80d39c77a2a2d52ed7f3e0ce5b576a89981b9d9d6aee05110131ad181c717291b23eb881845ba88903859be7f65fc6e795507574452a03d4e25",
        "041555ccb4555301cd5e3beaa6d0b8778a4505b72135567322f9a5a540e3b8a4fa127f16e181d7e3a75a2d944091c78caf9849eb6c3f3b24242c514e42fd30c0b3",
        "042349519b9c99cf376534801d42d098b2541903f5fd07e0fa81d71ea68c806f89086bad59e91f4341cef634582513b9359c751e3640c0fa9a205a6bde1fdaf697",
        "041033e55052e5ad95302c5dbd98a7be3387d605956d0eec74576a4251eb58f4da2534b51e49ce5768a4bef802e159fe1ffa37dba8437669d4c31292a2ecd24e4d",
        "04070ca0593d04d87f769bb59c63b76cc1478fcb5eb5528b2d32ec6294eaa155351aea25fbfd40948c8fd8d202e31c4a1374869cc9eabd991ac2e00f5b2baf4e78",
        "041d61b6c3dfba531cea1f35f652f6f94dbdbd1f62c43396dc378f70b6b0990e5b23b161cbce3acc6673a44939abc55b4a86f683e1e8ad4e0aec9e0e991c4ffd09",
        "04131d5925f21a50af1da2367abadf38f2dfd9e7257523dc4662d0bacbc0808f130dbf763b7934a0a6224c34de1b4d5a791d88729df242434e0145bb713a38288f",
        "042bfe71e528ee56f4c1c6f1c1de11864fe3d67e56b87dfb97cf608a83c4c2f18a2c2383632ed6378da76655cf8a5e151fc692ef5e07bfceb339c3d9504555a47f",
        "04058210b550fc16609877b5fc0fb3722a44e77de300ea96de918d913e952f0c401a03daecc90ce916f495fac309acf7c33694a2f77bbbc770384460c2c98fd13c",
        "0428ae164d26d0987c3c875e691d78b346d8c32a0aeb6fefe1510e5528e7fe05232a52f102a41d3dda80ec1eac66c6f759b405257bb836eec514b298747129b6ca",
        "0422b56318bed36b21b46827b3d39a6a63fd327d84ad09efdd6fd9b7d5bd71c22505fc11eb76fd14c4b5b692723e28c454f7db0a36eace914b2f2c87f9b81e52ff",
        "042a3e5a4c98a171667d6caaa396b0ccd03aee91724c0f3349214523861e5fcfa81ff385ef6803e70830ded0e23c2e76fa4d94ec16043290b16ac805dc2ca51153",
        "0420be7bffa5976e062a75eae9a4dca83c27207152d8e7301c92bf990e2eddec35166a2963ed3c15a5350c685cf5f9c6580b9b96de49afcd5842344350a9d4d03f",
        "0422e11534dc3c78583b6be6a70f21bd3f91b2d65f0776b88e871be1444c5323c21fb10a5e7f3f001a0476a99ed6eef5988d8899916f2e89c1d813a59d19bbdfcc",
        "040da396124abe233d7227258003fabf15f50e21fea5c48fd98c805104240a084113368c4132a31a97f20762b7c0fcdda013936649d410ed33575d9fd727fdd22e",
        "04278100c505a2dcdb395665dce5b91afb7d458deb9b2e148f63671f8bad4f67910271a00bb8db2441412cbe445219773f4be7b7d628a2123d667f2fca8a05055e",
        "042ccfdef921ed73c7c5bfc7e77f630048631e0e1d9dac267a2cc55fd15d9648ed30380375c926c49823159426aaa804e7aae72012d0a10373466c6c09c27ee0dc",
        "04016b16f7158ea78ed57cddf9eefee37f652faf139225b23fbbe72fdbeaaa1c5900deae79748f9742b576cfc8936fb1b24c86401e5756457791925764e4088fc3",
        "042e27be22937dac068c73fd21b5d70df22a95a7c5fc1902f28ee36f1c1211c46421657c8e8d11664c0dc1d0ea02dc0126e0430448cf415e1d7d2449dca37a06a6",
        "040d3b6892d20ddf0eb053e3fb40b71461a35f89212d25b8e6ff4c7b3e4272d5a61e8bb4cce229d8035ca37cf6a9fabf103299ce19b05a2cef38cb0948dee5b799",
        "0411d389c11fdc323af24c9e3488abb5064b1b0b312f641c2041572777922525ef26f06bda6216d6310b1d2d9997b1d721b34f8b13c5c9c06fa19badf43da68e72",
        "0425f96f8440bbe27602bcbec4ef5ae8d1bddcf2933a915438320c8d652823c9902508cabfce8c45cf54c9598cdf75371b7d55dc73cabf16e0199e83b5d06d203c",
        "040d6229b56cc2c4005612bb667790d1e5ef7d7737ed62c31b97b84d6af2e160ec03190f4f4bb3fcb136b89a99f82f4941b1c54a2b3d7224e56e04f9273c0b8d79",
        "042fcc98351a49c7137bbcf3644b6961e6b40adc959207dfa5894705da09d3b898028570506c9076b553b9399a488060c7b80c8279fc461ae9e150fcf55d4a42f0",
        "0400662d7bf0d66e45ce36e706f3c762933ed4ab09e664a58c557c3323e1eaab67118a6509dfc87dd195a650ab7781c410ebe0fbcaf1f462ab4f7966cfc705463d",
        "0413aa3bc49295213ae2369d60baacce80e2468b482a5e2a36233d9cac99c2d3f00a22280c564152ef48f9310f91a58658b39624b5d0f44b77f2d7388ed63392a9",
        "0418c6fc464fc1098293f4bebdeda8914e3eac056daa6c6fb9f0178750810cbf8d22f99251d98ea9e8b737863c65534759143af10ed2c83067b6e9b4a3dd713672",
        "040edf342ebb44b3f2f265e649376826fa04ba65e7d3800201066ed794f30b6ddd14c36e6cbb4125b46131f589e32d766f57fd36c34359f58b104e96a81473e2fe",
        "040d668b047386cb0acab1550b0c1afbeff2536de23a689bf1e129bc2ac61f6fd51f69419fa97ec0382f147232ed59c682df6fda581e2d2009522264fa67e213dc",
        "04283c1e0f0f38a5728c609b5e1ed6192ff14130c1d47245e1c26762566a4e93500553b00c7ad4aa30ccb8c2123cedb190c3d26630430071914b51800b06e88597",
        "0418799821c0ff5eabbad869f09253e0a7fd4b3e7a55aaf549b3ee84a9a198af4e2aab3995cbf05b1f4bd826d04f2f51052b620cccc2a3c22b83bcef70a1e64c73",
        "041258ee1a09c598dbaeb9955644fd23f4fc6328f1675c0ad6c847e338e72d086f16e0e91972ec2d221d9c08269298ab19fbb0cf7007e56936fb8b665af0c936fd",
        "0410bca800784c7b06518136ac6593c81187a36283a4164d2c827ad02f49610fd9137495b1e03a5c3e7d7d7980b16d6fd99baedce9cee07389066f0c68fc68d444",
        "0429e65fad8bdbb365d8001660da7e46c40e6b15c38e69066e1d7343e6a1b2cc9d248e0bb624695732a765f71e95022aad7b2961a8108e258b4da9273983450c93",
        "040a9bd379f4bf47075c922d7b4ead1f508c34d6ca473f599bd552c5858db58f8a05d0415d73bf2de7449651e777c3a06c73755a6a8881561e9c11e9c030fb97ef",
        "04127e9fe4f365ce4fabc527f22e215fdc95ffa8f43c2423fec2421c213e46dd0a001304a6ca915ac381d1defcf09faf4dc6afb9fde0983f5014a7185ab8a7f855",
        "04032f66d5cc0b6dc7c27cc507cadb19bb840b8c6a12478c439ff2a8fc1af14a4e19fd2ef95cd96eac5d16a8d0bc91c3f68b4f481ad31e5d422f91b5855dcbd1c6",
        "0429af69da99ef4ed6d4643177a965008880a352e1cd65097baa5ddc68c0729ffb0b166d20c0cd537d0334b0151a16c4a84ba7ac5dafbd802a765d3a69fb50a18a",
        "04023855247b32407f9a5bfbfcc7733e37b1a4532cfa25bf013c93bb36042cd6a612c41afa730d0f79a56b45d5b31260c79f0e8406e7326cc64a5ba6a414988f6d",
        "041d590dda59ffa35ee80b36b9ef648a612371f969f9fd2e090f6a7bb06fc243fd1287c81725da751779a0a27ccdf7319dad0579b36ec50aa23af7f54b5948df3e",
        "041c1b3fb17a7ca5372d347b1148f674a7bc53e24dcc7147cbe057735bb7b1e8601aa4254d52c25d0e58cee341ff330bbc2c1df303c3ad6846e2da4a4c9b00e620",
        "04037760bf6086d972002ee9b0122cc933765c20c51f08c7253b40df056a74a3bf2f81e7da90dc63cf09bfa0c249f3763741bb2d7b4a45033774abe451eaa3df54",
        "0409502fa9818247c38d09ffd257915d9371a4be3c957c6d490548726faed2d64805fc11694e318e19f342221696736184dc33a41fef436e237c084b45277cb24e",
        "042f55cd2a97b83fa8a4f0fefc89f1c72a49387595e98ff0cfe2ab19b30f4986ec28fb033ba715a19674c95be4946fccbde8ec8575d76fa9c2436b84dc38ba9e34",
        "0424b087bc584dfe89078b53b5f5ff46c46469143b83157495812ba1ab472502270d009d7f3efc72c50ddfa885ba63535d4b5b252861aab4b69f5b9f124a09db20",
        "040214dd33fd7456040855bcf76c0fad63483dda6b16bf7ee4dff4c9f2b9e57eea0acab70e80260581971d5f4f89c7d2a4301d7861dd4afa79384601fd6be7c204",
        "041288e052afbafb93b9dc4f27cf1b784964e75f53d8fc6a745fe80f6be21a89fe1b2937ceb73db1bc37377cec36d4923cb90d13e7f266c820e0f1fa4eccff87be",
        "04083437a88bb12b190ea01231bd7a8bfcab248718102d7aa57898dd3c5e05bc97040af4ce25a856774c0787e1a4ff1a570e59cb4193d15c0df1c30f9a07b058be",
        "0416f6496b027c9075d10480283802830d5a3aaa9b9757313ed892fef671da7fa405807d9578f0b3ceffc3a3da85febbd1fa050cfec1d73fe75881d0bc86cacb56",
        "042276d5f089287953346046bddf1921e329fc76bb287e6825dc34f4bf8f58dc0c1c1bd1dc93e17e227a672d3e7836061842171169d410ec7d58c4f7188c40a7d5",
        "042b0204c64f406ec4db650ab811e8402e53dffbc7009858b7a85e0d31b4434d871fc2c3c493700eafab3064b9c9bac4c7c9849272acc57a6b15e3074b7b919072",
        "040f7881321a7953f9a8219f2ed0b286764165a78cdf967e4ce84a0fcdc1575f9f295a7615a5dc665da1586430fcbad27b8f404267a416a70c17cf2d0ec390773d",
        "0419b585abf30809dfbabf20fb3a5fd3445d2b85a4ac5e18f4632b00a0a37cd8ed23071984fb2bacdd1ffb966a5cccf7cf98809c3093f7f729ece6a9c8cec49759",
        "04295e9611f727e86171a39a38801143dec83379a5c3eaa93aa3cbe3ad3dd9190c102f8dbbfd51c644f7880433149261ecfd3b4b373ea402760568c672eb7856a6",
        "04179d49d5ab186bd6d3091ad55108ff1331274d5acbc679a38bcb287a7542ade62e1bf9123440294b09759b5fd64c40297d03734c62f59eb82457eaf78800353f",
        "0413a646c75f2d8124dc9dc9ba29c1f0c0a78f466893cc50216d28ec5dd49d218c0378562fa539bcce9ab0cd70119368d465ec24e60d52d05ca639ee627256565f",
        "0415afb5f6bc5605dca2a05c189e7a7b26c2591de65bbaa91c0fb6170a0ee22ad812e7378e3d02f2f992b854a7d4a41fa25135b35710a00a6a1f12ae13eb8a621b",
        "0423f693ae96a6262169509e708bfed577047b79ca6c45ab125b2ea44fa8aea54403b4eda30591c51decdf7bf53a1cf4696f1bc4f4ce3e8a1609f8a40818cdbf9a",
        "04191a29b56c5bfde37cf0b55893be804e9baa9754c085e3ab186ab7f55a1361482cac2387a6bb92769a0336bfd72e10f91a4d397b92cf9e0f4465b98cfacef8e9",
        "041e37b6d393bba15f9c3c9c42b076b97372becf9980ecc6e789ae684fe39e5c9918be3d031141caf7a57a3c7f2bb3bc5ea500e0818d3902bbd7abebb8ef66eb78",
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        "041378253dc2f480760934f0f04d54e49f2099fa2c694de510ba05aee1f841cb980109bda84b8ab6261fbbe8848733ef939c69a67523f9cf5501852000fca52574",
        "041ae5ec96dcbfa223f504eae49bd7e804fbd0b17a968b701a2360f375b7c019ec1ffa2788d9996473a854b657a0b3dca8e14287de5c032c2127502f9d516e738f",
        "042dbffb2c2ff6c1772eb52647c6eab4bf72a7d8e93ad0156fbe4bc2e83ffcb1822a5b10b3e973d3049a5092e10ebc4bbb62af19cdf21483243f81f0703e4a7ee1",
        "041db4578f2a48385a7f4e4333a3a99e0716657c9b2087ce3ee0b6eb2052311d0408846afd50ba1bb0bcf1c511dfade9a9b724e6ccc8f96598773d59d047c7b135",
        "0404d9b7acf40cc2601842ad5df57cf8017c7e61bb0aa3f5fbe2bb17e17ca738431128987bf4eb7873ac0ee3493ef4a12bf1220d9a3b2c6244385679aa17c4b07d",
        "0400fd6838356358072a63dbb2ada3b9c1580b7b27ffe349bb8623c7254056435021130c8ea14ccde0d53bedb88e85e2b104326a94cef98e62fa44f8d7b727bf34",
        "041695a424a7ca05f6b86265e4cf38e9f994295901aa00f55e345cc1f256f2a37e11e93a451fd6473f8647cffbfcb8e5e88a08fd27be3075903e75573f7bfed3f9",
        "041b65de7d91cc0f07a2f1400986ef30776f82269809db03fe8e678ad495984f73266ffc1fde898324c2c45ba6a68ba01ba8ad4ed1f6bd7536ece655d0134e27d7",
        "04088989a891cb9e3933bc4b39f872cf7c4258a03b35dab2ad4631b7d4b3c18ade28c45749db4ba761ae208d76ea6209e4db6224d6449621e7ed71cf9802a1704c",
        "04299da297b4cb97d4a53111246d30e8139193bfa36d4414ed3f636761aa1380b20d710c8ad3ae2f1b0410faf99874a519782bb6564f1247d5e504b4d572414d7e",
        "041a587ba03087c2eadfe9e28de4bf3852f6f037f76682757c05ba38058ccb52e00fe96ee800a1dda0758f0bd8de09c4dbfdb43b3935dc9027bac1591993b929a2",
        "0407de369afcca2867a456489c0196aaebaebe5c8918ee0d0703f62e58b441be0c2ec36deb8f82eef0228c9b5f258d32fd4a1b20c6885b02d5dcfb76aba346e614",
        "042a58c7b42a30e920b8452ffda805d04f8dc9ff0abb50e8c1572a622675a9a9f612002af09f168d0fed93dd53aad456e6d6b1ab7c9c91c3bb5c91f7aa10811eab",
        "0419329242c09bd2eb48142f905e017a5b6bdb16923ba08fd8aef4743045db5f3a2a1897eea7c9fc6fa5b6d04640aa05402de9e182678dcd07eaab39014c5b646c",
        "040aad228124bbf77ba295de70bc7f706bef61408d9df745099df476ea73602298184ea4b758e80e8108d74b03b34f7493eac7e39898ecc649449dbf3ae8de5e07",
        "04120ebdc28ae75eacb634b08c899b8d69c5169cd546ce8cb2dcd71332c65b5aea23f462800f85090cf093b48313f42e2393ff59bf1961fc37b00061c7bea51cc7",
        "040e6e91db838cd81b6050d8450900edee1909885db64aa0210e7e8f880ce6710f16a95384832929b34715bc748fccf98823fa538cc2197d5f3aeeb9c38b60582a",
        "04146b6f644556092e484177c3dbf605fd38b1a9a2c0103a9a75a520fc05d3fdb8044b74a909c4a6b3c2331000923afd3032af41c5b5e30bb5748bc4fe761745b1",
        "0405f6ad5a1e1f550cae7008c2fc8fe429b0cf4bb181a0b7232a06bf32b7ee2d970e68bfb230d4fa30a7e7b3591e8cd3894071b1f9df6888f00d488a4f25205631",
        "04252c651e2c65e304a69f238f2ba44d8130b4b2759950239a1765985bc8a2148511e39d1cf7cea1661b35b8eb381a2a5697bd69bd745bbfa1cc8f039d3ecc9c9c",
        "041c470202c3bc79abeb8ac5dbbc9d7a32ec695269229c9f73fd8e34e076a7353928226defd9aba470204d10e989b16ea18f04870d24fd03ca39239c97448a92d2",
        "042d81b6e18797b962f46687512d92e46a4a07b4b08158ff0651f555cae926134819944530c26c6370a0b2690fbc844efc7b72c95c1543a8ac7551390e533e1940",
        "0407ec1a7f17116d5260d1aca211cf8d6d41c9e2242110965eebf72bc93e052d9d2afcb3bd2d0dac62f2c57cb4f261d924c69222080d3d517595d9a3982fd3af1e",
        "04164e98f79b15a9a0a96547151cc9a05c732fc7dd1e78ac44c6d68ab4a6ab21c42f708da63a29a89bcec03685a7d853b67739ebf01d3150f22b000c446686dd4f",
        "0411be9eb2675f561271541f1637aa3f7ee6e61cb7c56f2ea78786e2a5b57a311f2aa4fa347c06b24b8430963c8bd80cf0eff6069fbca1f7b8e436a11e965dad13",
        "0408558b2de18c446638d2da513f83ec316ca299b7bc823d3a7300a2f2bf205ac003b7cc869dab6aefd9cc8d91fc80d91a8720e2db7ce4c5fc57996e4dc1e1d210",
        "041594c1d20ece1b3433ca1ee39b4476b3637376a0c74617d610052ab39d5195440de80e37a34878badaa241710c00665059874ac69e485a9cc85f765b6f364a32",
        "04216d92167c9a925eb55403e14e01f428a266de374d923d2475d2ca44763de1d40fe8f70b4a8582a15d71735e1c86d475c754e0991ab021317a369cb55b6d7077",
        "0407bb9f4748af5a1a58f7303c9f4ced9f365c1b2c7b9e5b8dd9f4450ca078623f29718e3995657751da76bdf259548b1a4e42de4c5f7454513ab9fdd842b96b4c",
        "04058c9cd670184da6bb007379234e0fd2db702211f0e57f0af0a4732847a060ae113f7b29411ac80915bad1fccbbcb3a4036fbc3b8ec760dac65e95d3ce4499d4",
        "040b09dc346bcf005e484a0c858287076b289059c4b8983024548efdb1b446612e198ef0d6881c40c186d0a4dd1036283d3a21148fc0955381793979c09dbe0896",
        "0424ae3f2b0e02a5e62f07ed251e2e6f4a855095dcdba6973e0cb8068e0399ae652a725d32318cbfea203c0349926be5dda96b6965bcf40d2fc8dcf28ca1d326e0",
        "0418f85db37b280d36012b3d632655af37818acd26d3f728c7d75144f3e20b92f826f2d13f37a852f8348531e2e0879dcf7ff65806f3ea66c3b6a8dc0b1c39d43c",
        "042736509f322640b10fb1692ccb00c7b62569c98150e32bfca0bb11c7ae9eab8304ffcc57689996edda19f7a970755d675d914b0a6b6de5a580a4959656c73e7f",
        "04285a9a4cf39e825ba5087c6f8a510796bb6d9032ac850e4bf03c24141926f0ee03aba476e4c6ee490cfbb0a6ba7099c51e8c8d1b49d76d745f5fd2facd5e8200",
        "0418285e97e1e0e28dc1a5fc83a6e1c31ca5519981e34bf1319629184cb703f7861b23cd8d3edc96cdba32cbbcd4e2a04e8b6dded2c85e85fa2468e700d6010309",
        "041ef5b3b3fc4bff399672777c708a88ee42262673fc6c57e3a9bdeabde2db582919290c138b58db2673d5bbef77610797ba81085908b12163f8fb93ae64c1ab8f",
        "042c26105a9aab37f29b053e856954290848b78be38f699c07b294c0019603501d14a3bd1b9ad9c1969f6dd44cefa5ff983f3e6cecd088e98c72450513c89dff23",
        "042630e3f0ae0769000e292e99c3502e2835b465e22192fd8989f64c1735bee7d002242fb42015c31d3d82d24422b06b420f7515cb7022c4a90ecba8a5ee7e786c",
        "04231d053240d7dd683ac4197f147d3f3456fdae9e275b5d5ec70f49fcf32d84752abf113de9b0b66f8216824484dd77abbb28490e15fd1e996d72ea43078752ac",
        "04067ea7ab3c7436c0e5e599aad6ac93a8da911d0b0c8a4dd675514cf38c2b26bd1d5568576f01af2c14af20512a1562fd99c4964ba8a6b87f050ed48a0d651a3d",
        "04022ddb868647dfd693233aac44a9118c48c03bd625c7282e785ec39cbac810660da0f9cf03835c77517478b6da2f3588dcba969b8c7e0eab53a20bcabf094f8c",
        "042e6c41d5cabd81dc0cae667747f8f2a05c1f05547e0a35538e68ef8d6821e1440a39d78cc2608cfaa1899eb9b7e365595f0b1130af5baf63029ff7e10f814c8b",
        "043028979488a631eac9c78b04e3d46992f5bd73384c40a9a96c8738983ab592bf1aef71cac4a3bcc5cadbf67d91a9f8011d004f97a003578e373caccb4229933c"
    ];

    let mut acc = G1::one();
    let by = Fr::from_str("23938123").unwrap();

    for i in 0..10000 {
        assert!(expected[i] == into_hex(acc).unwrap());
        assert!(from_hex::<G1>(expected[i]).unwrap() == acc);

        acc = acc * by + acc;
    }
}

#[test]
fn g2_vectors() {
    let expected = vec![
        "0404d4bf3239f77cee7b47c7245e9281b3e9c1182d6381a87bbf81f9f2a6254b731df569cda95e060bee91ba69b3f2d103658a7aea6b10e5bdc761e5715e7ee4bb01b4c328f0cbdb4aada63b3d09100d792376b94d07a6004e46054eeec849e8de9835158a11d28483dd8db236ea49f3630edc9e41944e494c5aacfc36af3b66e7",
        "0404c5e44995c156973bbc9c517c2954432c98e22b9d8af8129c4493bbb959f1f43ed22744e62bacec5e12b5197d83766ecf9d13ddd439b54743c20a7b2268bc4805b8e51bdd262aa888b3a952241dea114cc3916071ca74cb4322da083ac8b7643cd9bb38dcc060c32db060714fa18880be40501dfc80b6c6e66b4ea887c22631",
        "04035635fa1d296fd5f2813296a966c6b18152901c7d4ca17f174c039b108da016f3d2952a109480cafa46aa447cbda243fd6ebc74bc2868ef17a0cc4172fe05b7018c20852a2f8ae214c36a3f7af2dd58aa6f23bd62a1d8f299e05b278b6775dc13dfe213beace753b206f52197124f6dc26fc2735fa619d82c9f76a73d78676e",
        "04020f5752540352db660927b16a0cfba818cfaf1b913ff7bcb00481aa326af3e513dbebbc44077a7214377383fc49a6ae4427f45c536efd87d2cfcd17eea48dc802af3d82c179c8a7424537484cc95aed68b867fe21ce6a3f424af9ef7347668735ede73a9ee3c25e0dced45676fb92ec3ac701c141bcdeb8dd5373a35f384922",
        "040137974a4a047aaff7d8922e9c706873e011c95ca4cb34af04b44d86c159e8dad574abd2a08d3b328a68888d25e12f472cd2ac88b609fc81a1992a19806ea0b2055d1fd8b46e206bf9aa197b321ebb4f8815e385fd648992a3fe398b71c866cfb99a82e8d024ba353944f1cfe9690a52875d41ccc31bfddede91f27b8ecaea7e",
        "04020c3616423f149d8f42911aa2bd7fb4626515699060d5a60eedad09d3c784471a18e1987207fb327901a11d49d7f355647c7ccb58ed9f70e22ded8318adf88d08b8e683dea5a37e32d6fe1f718ef5694787a7f1e67094a2b4717686c57af93001c910bb11bb8b2c0fb72ec4893620c74943790209c447351f408cebb39203b7",
        "0407adb74c6bcff2a6e93e2dcf22ccfbdfecd36f546b66f7426a02beae5bc30a20e8bee8c7e19c8482c04b6e99c3cb57d96a860d8596eb8625f1b56a76e4728eb504a1187fe5fca8442ee82e4ad454cf481336a98aeb006faec960bbc3611aa8ab760db92bdce1366f01796706e225c9839106d702b1aef979592ce659bada2069",
        "0407605071bc63eb927944572a73188043b477e5dcc9b98119019b4f64e4854642d008e89fcb2729fd1952fa345405db37e5297d09e642094e1457137eb6ac4e690471e1be5804a02749c828341edd1bc45c49c8af6a83dee52ff6c532d836b2baa1802356c1d52a75d2c5e90dbb00f7141041c0b16483ce8ea36e53de95a3e84e",
        "0404d6c1f937e290b9a5257f7354cd5799fc6344e905f234da2bb881c176140558022bcd05c79ea7c243f522eaffda6e0892b2b61e411c77abc3be8224796efafa048d157a147d2c2cb88ad04bca2dddbb15672e58a06e91ddad8a74e97bfe7f8fc96dc45ac3fbaa010ecec3b34ae15189c03012157dc749301408b2c6f988530b",
        "0400943766f49fe196008c3774b3e85f11f2d5de21e70dd6bb3531d62ab0fbc28c9cd88ccb261c74c4676fbafa12f4ab3a0be81307a3f25af502fe65f76c201048048ae051920ec0893a6dc088e5a3a5feafa37742aaf8a7bafa9901875d2eaeb6b61050f181b8a4245890e0d4769640672f134e2f55a1e39cda86a1d0fd608205",
        "0403cfb0a17f4cf3132e2dc785c8cb1db29c8e16bf9c9cebde73ecdbd549cd65dc392d458facd605190dc10d3acdca856ec2259d14563967e077c1c2b32403715907a9a6e8409fa5215c9c6aefda975a84abc8adbc85205c67fd1392a6764ff569d7eac0138396e8bb1e342d63a2bb24d1828ecfa06164a8622a141656fd88e7f8",
        "0406a7ce50c9401c52e3fc529fdc19ff3780b384ebd20951e631034372d89dd0c5cfc3e5ad93942577e9ed7231892f77d4916e36d0a3f23709da741c48b66fb926051902ba61d885f8c20d27d83a5624086f5a78197f12f0f038402e0327bc0b3ac16b5ee914752da5c67a555000585e35eaa78f8ca53c41a9d19b74f81ee15ee9",
        "0400299edd435f3693ee995ee9b7c8748a53047f99899ad7dc25248bd98487571cc2378f81cfbc23d978b6c6f1096058c1a59e076f43e6a8aa5f72cddeb48d58da0887d7b8c12062ec5c54afa7864404afb745b7a5c9de272aa2dcd595cb662037eb061b2884cddfab11994ed2de4eb762b0f65d306cb690a9457e7515d60c78d1",
        "04018caa1fd5b7d16d40a7ade751f9b7880f7dfb494a891480625ab0a0f44fef1c301d777b9995cf008dec8a54447e33dcf612ca6b7c452433fa30cd4b22d4dee608f0bb09d8dda4646bf09b68e8638180a09f3c7cb9f4c65a11760a98448a93d3d757e27abb67d089388a67f81977fe556b74aa30dfa551bda6440858daacf6ab",
        "0401e6530a4a66b40ba819df57294629c7aca9f20781e525cb0a14df22081510292456bea747bc1ce78f0511d4d0cd8f1ae252adfbfbb5cee8782b8cb86521603c03a095fbe813a44794d65f434cdb6b4fe99d385b9e52801732052a7f3fc9b5f8d662f5dcde8c3ed20c1d8a2f82afb66b15800a3e2f5380d60fc21b145d7231b5",
        "04010598a2c0ad659e96d34ae9d104565317d41d272dbf04c0911504c3fceb1638cd8f266c6875c3e030c30c1b048cbe59c02cd081f824650529f4d88671ad32430232cc5529ccdca66189c3a8b53ff2b39aec70fc4c256dac2a46c902f3f35893fa5235aaa57ebafdfc84c4368040ce03bf0f8b166ebe3df5b0431bb8f3bc5659",
        "040436842e04e15d2ab8bcd2a26fd1caac0cf6709d1160b133a42b5da710cc9d4d58512c31ed6f19a71c9c1ac5488de9d1110705cbb4a6d9b53c6f2120fc3a0cb503258a3ae8c2d63b076f4bd54aa4019ae5b34a7318f0719e1bfc7d48181812d3b864b44ff8959f0952da2d5e163bdcf5107117c734b73aa2713528f15647cc2b",
        "040017cfaaa9a340cff1ca650cca9648572ac1d46eb029a7cc007ed1277450bf7086b81ea6943077c70286f5d88df5c25aa64d787252ac51a16bed0d3bd0e28ebe01e7597b90dd4a4124613d2dc85f29b18972d818a54389f7b9ba554a34ef756f90e9a3b0f32afb9d2e3d4b79dd7c01d806cb7155a56d152402e57375f1283f35",
        "0403f7ee7e7f97329d2a6a113a982e46af6475c565cce75dc299941f49f30ea3d0d9095fc9bd56aa3d5876d8e08ba564a834cf1c572fbeff4380c33d7d718e1b15090fa3317b58fa33afc02e4d5b9e4823667dbfcadab134a679fb760e187f6185d851fbbc994813e26a587813ed1c3da9c616a2d3e6d9dc2503c94bb8b2ace5f0",
        "04058b81304e77ae59a78ce3fb5bace9fec6b110370add9b155e9bbfd7af68d82510a364c966af4b6b3e1293d80c764501249d100db37a2357b05ae07b9bad296902cb6de551325e5f35a196f5683c6e285b1bd08c4c169eaa8be237815c285fcc79a680575a163b73dd592d6e565930eeacfba8a4d54120b950b2436697a4e7bc",
        "0407921512e74c698b0971c24fa8afa88d1e9172d8f818b5f7d1d65ff617777623cfab51a72e82b9153e1444d2276d3feb87092ab7b591f5f3665c8b89e0e2f9a706a09aa97351d637fb62d3de39e27e0b944439b589f194949b197151fac324b0a9a00dc7c5698d3814768499b1b4d073d8df0d26233267a05819e9a532cccdf0",
        "040510ba5805ff5e8b0c809460d21fe6aa70b02c30f85adf382e3078fceab64bb1101a617f8fbdbf33b7a0c2d9b7d2f6db011b63d94a3ac8027a36b22079563f0a0608cb3a71b579e6f5e36928642e61747eb286569f1f0fa1f025f24cb860aaa7bb6e76cc394877818d73909ebb8ee8305e7856535d133822a741b743414873aa",
        "0403f27102a98d71ae6b43d51b81cece07b926f7baf4f11b7af4e87998a5963d990d1da52aefbbcab8c1aff65d038dc56ddb01da019924aec53d4cce0a70c68e4e02b514c07515c6f29ed424ac986a487caca23b16e66632ce1f14f54f8f1fd4f87f414b0b5031e411ada8c3caedb0d3d8383f676ef158b5894f80e12975d9db56",
        "04038e3e7d9d44459f74e9203cf2c45b9019eb783e5898fa56a990e031e6a0f578e8b403c865876b92f53754c06f7c70f11fcbe4aa6db36abfffa7bfa2110b99130856b09f1da0ee7d3d9eca4bff2419921aa98ecde0b70ecf55061b9559f4835aed127d78c239bb0a324a628e4866e78f737476fc729eb56c0296dfaf182901c5",
        "0402b3dd1407e6ff2faaf4907117be8ad07db0caa1ff1adb3d1eb21ae15e3fcf6323aa340f78bbbe6aa3fb72319225e040e7bd4e5625567c72e6f65a7947f3a885060ddb3a00eddcb13db8b627bd96e22e905b913a50fdb75192225cd712a957a403c8479178e8017965a2517ef5716c814492618ce956c3eae8ac289dc88dcefc",
        "0406d516c666e3241f96315805b77415e3ddf8cc7139779f3875eca136dc1cd29c823fd2f8210cdfd7baa014f0445d1c0100bb8e0fb0b38c5c6d9cb0a76c769dd5080966fd500bdd602f2a6cb5135aeec6c56c48933e7d7aa5678c459f8f1cb43ff24f8766c67698b4a186a9a44bedc953997808d112e45313990d2ccd4a7cbdea",
        "0407e09280b7559d9446944f12a71b47591fa16848633f4f6955f598d1cf8e87db334ebb8b93e5c7b37f3b32b1457c7f728f91c33d175d06b6fd286f996194caac073ff9d3a8b3e3a7619bcc4535122a322796cd21d458d48c413b382458fd877a32026b2e7ba591b03b529fccde37aa98d61d9014f7f1198545ca7e838453f7db",
        "0401cd93cf8333ad146ba33d60b66b6b485fcdb401d5145e2cc4f6981c3d376f1665b5cbb8aa2d803777cd0a0538eb6460c80467118c77cb3fe6d467500bb951ea0137efad28140fe7500d9c75869333d2e929a980b5bfaff0be33dbf66bbe4646de8b2ddd928afa7eb7dfdae548bfefc8bda7a5ade663c838fc5c03bd0fb79204",
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        "0408e386ab8e32af98c8fc1a7212a48291d309181150ed90c3d1866cdd4bbfd35d93a8ef37ef2ad239b65d1f46446f4de37cd64abeace7e45d93190db348102a3f07b6691c6c75438d5617f59af8ce33cd3639d1fa9b1aab6ab2f04a255b684556b2a8bb2c5edd92ad82ebc94e808752227cde7c8bab970119d2f36a13d5cc0d07",
        "0406c6ca39659139e0dd9e257c56f95b03c6b93dce0da90de7cdc71bc01e721c7ea1562913c7ea207eac6808c394628de85e720f3f18d71ff36133753859c58054061020c407ccb5865137ab23d1fff6e8d064d45783a015fa4c6250bc3c07784e9b657bd972d56b8311cf56e30a2fc8145ceb656b285dbf14917f206165c1bd2d",
        "0400d31dc557bba2ca2526bb4409b5d1ecad9c77e1a5b7b39f0fc1f1a602d257e9f874c0ba04bd0527822e54e19924ea4067c8589927181811d18864fadf152f0a0158c8d26e97ade66a32ec3d164980ee3fc647b9c7077d7d50b7d084ec77477b5fb412b7bfbea628e2d171b0b8c100d5aecb747ebf2281f6b114e0e9e5daa4dc",
        "0402019ad8dd796757f4273cd1567a1341efda4d2c9131db4c38048d232a9672897359e5aab18f42423ab47ff09f28a89e551097aa1ece35b98c8a5fe8ddd33a2e03a7e8487d3ce19a2ddec76d71c14eea4a40dbf77094cfc1e2dd85b38e790519ba62cf66fb814ac5c968322d5e71fc78162e6f59ca4e04834456c2c791dc6d38",
        "0405150ccaaee1db53f4e1c0ea58605a54066225a7fc23ae791ad0146b542031fd57ba29e4ee15182586b6df694f9739fa7fef7b00af88c19ccf872d2c66d53a1108f56e65b6600a97ae0ef1a4857b08279b0204dfd2ad813ef5c34e6bdfe27fac8991bf3806f05f0d035d44226178dd216219e7e18b129d3709c58db179001a9e",
        "0405a9c9dbc173bc7b6c232c48441ea1c4930a0371e00fa244b38107908978491f905769c86aac0f84800a617376eb2e1815c41d2dce4fee44b7c61565e13a2cdb040046d3dd09566d83190f9a966c84c8b0289f304737fb48cf9ee6c955c781bc0fcbaa1f136c04f5b146f8785aacd69a967309b2f69b8488bcc830675c8be3a1",
        "04020bb3383933332a409fb39ca5aab2ccadb68681eccf43530dcb63f9cb3743473fb7f81c098d0a86e30a259bf3fa3c6be71b547f1e754e40ca0501b0bea07d44045fb4e63e8005790237cb3cf3097d8e1f76a649b4da577bf6f7f1521ba36edeb9c5a530407e19519b79f5569afb15313fc8556afb05e64df2d141a3a54bbe4a",
        "0407682c4d8ded1e378053cd099af83d6b78b95d3d8db8c74a1502e4228bbc553a2f0be6b30510b54b95847102b09d0c3d9d29b8304cbad607c8c38b58b239e1130292336e90b0b012ef16c0b5aff27dddb45802aa957610476ed64a731e9b0e24279198575ccd0c176fb41942f13f7eb71551160135c9914542ae5942a8385e91",
        "0402d45fa6ad245038e2e474c8febce5e0d483bf0fe9da58e67fd29eb0aed9278900eea9f109f0961bef25d9a95b06247b2c8b743257a45fdaaa43f3fab9e7d5c103d9c7e52ba0c1b9c31fd288cf84052a28bc22f277c11ce072ef7c65d49798ccfd81b41595cd0ef89ab1604371e399a00dde3308ca8ee8074d71e92fd95bdc97"
    ];

    let mut acc = G2::one();
    let by = Fr::from_str("23938123").unwrap();

    for i in 0..10000 {
        assert!(expected[i] == into_hex(acc).unwrap());
        assert!(from_hex::<G2>(expected[i]).unwrap() == acc);

        acc = acc * by + acc;
    }
}

#[test]
fn fr_serialization_and_deserialization() {
    let mut a = Fr::one();
    let b = Fr::from_str("17").unwrap();

    for _ in 0..10000 {
        a = a * b;

        assert!(reserialize(a) == a);
    }
}

#[test]
fn fr_test_invalid_representations() {
    // modulus - 1 is representable
    from_hex::<Fr>("30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000000").unwrap();

    // modulus is not representable
    assert!(from_hex::<Fr>("30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001").is_none());

    // ridiculously large numbers
    assert!(from_hex::<Fr>("f0644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001").is_none());
    assert!(from_hex::<Fr>("ffffffffffffffffffffffffffffffffffffffffffffffff0000000000000000").is_none());
}

#[test]
fn fr_vectors() {
    let expected = vec![
        "0000000000000000000000000000000000000000000000000000000000000001",
        "0000000000000000000000000000000000000000000000000000000000000003",
        "2042def740cbc01bd03583cf0100e59370229adafbd0f5b62d414e62a000000d",
        "1eced988f1c4e0f7f7433f99dc0eb1b89dd2a1b7c00a6e1a5df4900b27c8a6b3",
        "02363a20539db6638514cb4ba7ec49c91b2c5d405b7e5c021d3a0bf834f2ef0a",
        "09889144b32647e7a6a9ec0646bbabe83d9b7d9188c3bdcd3b002c55c9aa80ef",
        "014ced1876c520cc926b880803323cb80b4554f8c2588032f6cb727157371641",
        "179da4e61ae3117b9b12f86f5aa4f14e1fc3b46bf05d1423900f9ce6228b6d40",
        "067140865d6292881384dc2252b9dd20111c942dc2364e8c98f1da3c28da888f",
        "2ca25f36b7b20358489b49421b20f6a10eacf80e7f3d2bfce7593d0777fef418",
        "2bf0a17a3fa0670820f4f2469774a98f9bcd6a5e490e97d6e11f361c914cfe8c",
        "29a228ca3b4b8ed9cf1c2957a826aaf9cc3d1bdccc99996092b42907e8d763d4",
        "296a1aae3b4d8c87257609dba587338419937a3f7a8e37234deca0eb9b761478",
        "05c9dd8d3da17bb45967ad595e6440ba84243707a5b2a45568f22731b7f2055c",
        "2e99a1f1b911be2b5eae798a1bdb87ec8b6b66015af43114d4c4f0c3081808d8",
        "0500c67659a93bcd482ce6e2e198e671bff5e9bf276891b0c7f79200da6dd6b5",
        "020a4cdd4381c2c7e2a1885ac88036bbacc0d6aac38ca1113c10efe9226e5744",
        "29329d9432d2146f11a0d9e2578c09f7f1182b9cb20f988c6bad57bcb614e48f",
        "09507fcafb26bb82d68228ef5f5ed7b71aab295bbe4cdc759df141917d11d79e",
        "00a0ba7dcf0405380408feb28cdeeb784a19d0b9679d1adc005e9f1ab34f251a",
        "067517b1a7f50aa3a3c9dd3db988b0e2e87a8e6b3fb1184b8a06cc3529141132",
        "13e5c7527050b265295b9739cd2f95312932bfb62ce4c159c0ab92a61f0dcdab",
        "2a737c37b6881ca875205b949c313108f54eee116d876d4685a88e77a88a7589",
        "1103f082a016eea4c4dde6b7caf6d5f23d45007920eacd4ac8c952a9ece70d33",
        "12f45350d4c50366dd0c88a77ce35b802cf1e6929210449ff83a73a627ae8a9b",
        "18b04aa529992886a880fbabdcc834a983bf07bfb23cfa7bba660aec0a10a8ae",
        "03820dad30db55157ce87fc6812ec0a4e659e7547b18206d5844a6d1f28399e1",
        "030dfdd27e4e180392ec965b8bf2586d3203fe8931be034c966c37433625fd9a",
        "08a9b73efb3282526bee3e609fb408449503b70f617b3bab42919108852cf44b",
        "184b6a8fd93b49422099e5d75090dce92edf553115452635bbc8e623ce312ad3",
        "030273cc32bbe84b480930f2313491a19c00e2dd39fbd30993603bb8b5495e95",
        "1622dd450399ca70b99e94f60d87490b1078ff0dc3ce82cb32fd7dce0c4a4499",
        "0195e53a05f7b95040d27b2819f7b23b40c0871dbc476e3c102e4cb64904483e",
        "2910b512191aae4c5f27f90aea2f41b3b0e0f2042d57ebc8dc51901d06b10024",
        "2e795bc0783c41c950330abcbd7e92a6d7e558787e7f579b4c2e4aaf9f66630f",
        "0c34e777e38a18cb4edc5e9d3f4f07dbb1b074f38347dd53a015be494f24c0b0",
        "277348139e45c362741e424e4dc10b94df979bbf14f7c4b6dc144a0a0c593e1c",
        "1dff63c029e19454c2360a88baf804cafa60f6a50cbb71a79715c2832cf47408",
        "23e84f6518e9bab5af850cf1f38a873fe8be0c2f786d1d4e1fdaf32d46150500",
        "211b26970071c65390a8c6d822423ab281aae480a12a6fc836b40884a4337e53",
        "296abf4e45cc54ba75225ebac4fe863d5cfe725105cadfc9f9357f791d7ffdd9",
        "22cf34de7b862a2c4874a03b7ce9a9ac8e748e4741a7d01ef7e443430a543b33",
        "2fca5ad500e198625c9d542e0d4aefdcda28d246edf9a83f34c57ac1cfe98a34",
        "2a471ed73102e6918e55b0ef00822a5281ef0e49b4586cce10ab2671ddf95731",
        "2210b49819b69ca317b63ccfe3a4fed4fcc9b9b368dee5d988624487f7cd7d99",
        "0ac117037c41ac977dfac11e614ff3c1f0604fdf1e934addd96ca426a2d56c45",
        "18a0c2a40073a85c4a4cec75dc9e049a18def78960c7429a9c6abc1cde4d1c42",
        "229574d27795392985547b551380cda18972a32c2caf87b910746ebda6615ca8",
        "1c6f0bc008a80d5d36cf483df553e24ac4f969d7a02f45e93181441d79fb72fc",
        "1060b506a53a740169a80954eb5fcfc6b261cfca0c021a8113841bfa2b10d3df",
        "23ecc4f3237f76dc81fbbb8e467d253ebb6b4e99b9f2c607daec1bb599a63108",
        "2350041950c0d7144e6790f939fa4f2f53165b82e6f5c1c730b7129ff1dd6075",
        "179de2653b84e8e5d925b21cf206b9886ffe9df14dd300ef48341707f3a8e43a",
        "16c670be2c945714cf9e5b30cc54b846a86ade34ca2f19e95cb9782cd1a1f4f6",
        "2a6ac3b3bd2a3ca35792323fe39384b7ba44fd70b8788bfb9a28f0397e6c58f2",
        "27c800eb72d3f1ac091747cedb323b02178e9cab5951f1b1c97b70430bc93f49",
        "0acb5953cf1583df3f5be7fc264a01d561642171ed8ad66cb0750ef84637919a",
        "239f76d1622590038d64e710422cda6cb6e3e12d1593b07b08faea2dd71848de",
        "2dab87d5e027c3aa07b95691cf313088176763b92a1a101142b202224c889319",
        "2ebb685e594b7ae133c381606c8fc1c7a07ec46c653b1d5e73734362bc8cc31b",
        "238274a880a47a28cec6660f31ca766e7c024fb458f7e1df5cc8d9f1fa49b364",
        "27c5e092fa1ee06da63928770d5ecc7931845869260b3966d6523ea526db2789",
        "00dcdcb4cc0015ab8b8bfca1d52e335275b6fb39b58d41c2b30367a104dc2fec",
        "22c7f9595340b66a5f0781fc8c6856facc2228ef749ebe8f4e26a3c9ab74465c",
        "2ea0cafc90188c763ae65f132d3d5c873e4bf9a50ceb079874d1c346ab8fb63d",
        "180066c34e34c473953b3e66d98660e733729376074b231198e921d4ae28ac75",
        "0cc81637599da9f5b8285737283752575daedabd7b463e02992933126b59e167",
        "274ced6e1efb4148e7fb778afdb6e7a41a5af073df6c43b7103f291efac8ca76",
        "2dccf0cb2b0c9165392462712673c4075a99d1f1e3118ffb3deadcda415768a6",
        "1d0128b4b0f47f814b2fb6491f03654541725612c465267f02b73ed28074fbc1",
        "264770a08b4fcfe8dcde0161cb4cfe1d851227fa5538adcdef80827636d95f92",
        "08cd18d2188a1b7e7103b95a1b7022cb56f14916b5b5a8b4db2b7305d222fb1c",
        "2b0fa450d5c7dda8eb466723cd25e0b762968e52fb8a558225ad2b0b3c9f15e4",
        "0fb89c9eb27d7e49d4988722e645714fe5be1fd5d1dd7b9f475a10222aef9fb0",
        "2384e79d245f048e6433b04a3c7e527a736c198c67682a23cccc127e0fe341c3",
        "240c04ce80bb543b5b9dc19abacc681c8c58778141349e9e3f492515c54dbfdd",
        "1b2c3e4505b9325d56c1fe596f839bc3bc023ca08485a3f71f575994e61e4e9a",
        "2c341055bdfd39ae1c9012b5456790d9e6bb603a56cd215b8fc7ff5df23babda",
        "2a618fada6222167ec179c0d2d5a3db64b07d04a0d8ce903ffcd878708131fc6",
        "098505eda76826a820e63e004a19ce3c16fbc465d5c294e4710121781e476016",
        "2198b95feb3a29a0bc7439a763caf039448143e464d12c3a5753fa4b4039b97e",
        "23e150228a041db5a598c4955ad4b763b2edb6208b5f4caccf790d0a2d927215",
        "1806b48868d9900275573f4e57ecc9257f0b8787527a2b96d2e24f1cfd4b6ac1",
        "2b7b0225bd8e48a401ab3a10507845bf3110c5959980023d166dc4be0aabdadf",
        "1b5d5b3c9f454b4019116206d223c708bba4ee71138fffb32ed8674943c72486",
        "2a495d1c7fcaa4f27be5914c7c6fed4fb65ee46e6d7974a55141d9bab30b39b4",
        "1fddf00cfacfef6cf8dd5e88e04298fd376934a40938aee523338677258469ca",
        "01fd18b9683b1aac8675185d5d06773aaab0e19112ddc9bb63e2c63bcde49db0",
        "140899d53f48c9b200a48a8618dda9f24ba27a9acdb63dcf633107feae16fe98",
        "0a0a0501eb8fbabf040f420ecad8797db587601e3deab6a01ce4b0d306be7cc6",
        "2fa5a098db8149032e6bb899bc0b97c6b2ffdd6cfcc955d17ea2afe6a3cc3990",
        "26162db3d4a6e6172f0b8d1d7ec1f706f9eeb7c6d3b0c2a510d7d0e04fe4eda6",
        "1fc0dbbbbdea0ffaf2864ccca1b7e937efadd6987ad73881c5fd534ce2ae55ff",
        "00dc4562c8483647fe1d924d50c574fb00b53973333cf3f42b24cb0412d1949c",
        "2fcdf1fcbdfbec79a47715a340effb55d042f522b0b86acbd4c2c286d8afbbc1",
        "0b11546ba7759df51528a4b9656d09ab5c2b7423ea82ed36d7acb01fe96cc8b7",
        "2f3dc23b191c92d0a582a35f19c25831bc60fe3aa228c3e00e70fd371f72e80b",
        "17b160611d7b3fbffd972f516d72b933980f325db9220cb1f953f74d166badfd",
        "17e5ddf96d4c64ebb06179a3544afca2bae78fc1089031906aea8afae5610147",
        "012ae487cf528b8197e4333b56705d7c31c92545607e6edbb0105717f5e33f66",
        "03a07c50c596fe0ebae61d554d46b055a6fb0de2da4a5434e026052292ef06ac",
        "27d9bc26fda4e6554de6d29b88934c53cae2eaee241ae7be961598f41118a7cc",
        "0a772b263180a8fd6c99db42be795b3d2944d4858fd84d307cc438dd82541cd1",
        "1ff90c2b7d3df22a1dd77b407e7f499d7ce6c7d5d3dfe360c485b6c49ccefcad",
        "0253973b5ebdc95b42002fb7695d51aeb1410ba1aeb24d98fac263963e527daf",
        "29912c9332807ec705d49f06c24b30caa6b9cc764dd223510e0fd21faf1aa1e4",
        "2c9482d7500b2eb22073cba5e6793b8bdc684e2b979df3b18e340ac27141b147",
        "25ef1f7f3369c7490da551cdee2eb521d4c058ff26c9ce503174f4b776a62134",
        "2850f791ce002da71a143489ca75f103cdb06faacf0cc1cb42d3f16f007c6ac8",
        "1b2dfc7f783b9a94a2374d632c7f2b9261c64f3384e7879f8777c761a0f38916",
        "1dab259a8cd28a888944dc62f0d71f77fbea3cec30777146eee454d8a38862e3",
        "0ff237bdb85a4d1d59d1771a372d85bc4c929c13bd11dc5ab547efbdac506d72",
        "03ccca3ce8529946b5971cb7b6cee1b7f0603d1a14fdb2399a0b754616881106",
        "0ae33319df196d3e6a9d381c5e9216bef5f269ccdd9bea3228bef871ec64a5ce",
        "29c85de273bf79ddd69170fb339c8935870d452eea31b4814181315098fe04b9",
        "192ee992c2734232d8cbcab87466cb7e4bd75498bf744bf0fca69ae2598170fc",
        "0adf8249950d832031f2c04795d1be24b8e819970b3bcabb6fd36c577c87d171",
        "1b91d0bd5d309d5f45f5df4d86d97c1958157dc4cde3c9328fb649d4c2a2660c",
        "0e4c23d81ec837f232fe6760a9bf81bb664af07b329d66e89e6f91916869c3d2",
        "0c53fc069fc35d46b0c407bab69c9b6e2fb9c5376628f2a01e0d15c33f0594d3",
        "10c10f5778177ea594ccd59c145dd1d6b98d79f29ee7df7cf350250629ea3749",
        "0591aff9a9a7aab76de4b8daaae1c7d99ed89fde5cdef42b7e043f537bc06cbc",
        "2ba5d15ac6497c83a9febd0295a25541876fd36f81d09b0042cb7237d73ab5f2",
        "1fb87964fdc64b2daacc9dae6e72c02785f508eef8b768518f3454e330dc2165",
        "0aec2e9eeb137a1c543d268adecf786041461fdc60744b2f22578e631caab5b7",
        "24646eb97864a13313b58b69196a7a12b9d050b193367f130eb8c10a49a186ad",
        "1dec3036641c822b85e64b8de5bc408c76c6838d0a3014a6e27e1272b9bb9483",
        "18c693429e6f97f4e5c28f4919fccedc3a1bcd5ccfee44aa43016d433900b84c",
        "09a1de0b073437aa7865181f666739ec4c8d44d97f68d2d7d5e5df25076f327f",
        "05db3ad1ab9e2a28de04383ea7b230236123ac43f1bf7eac680dae9172008971",
        "07414b2883fd13eb65025bdc1f9009cac40a35573dd165ee02cff68131ac324f",
        "1a6d9d6e44d0fbc16e3e6dbf6c3155f2da235c111c4a0db70658caf85321918c",
        "1e2762f9794b2c378e80cd7dafb47e5de60f1c592ed17bd50ac8d893a1ab8f42",
        "12ddaeb6d3f21d798299054a866e82a2c687fbca1cb831d6505e0cd7c1f641da",
        "0a4ca4d5033ad947d714f58dbef044e956c1df7061805da40d075e0626a50650",
        "194cb0367525c19f645870790da4347d1bc8376103b185744a1fd253fb5df988",
        "13612ad38e3f776ae2952123eb8a366f969b168789c313c3b59bce858d1048e6",
        "2a9f4b659f496117b4a61752f4eb5f8c75e529a576c975843481b308c6192da1",
        "286367a78683c1f6b8d510f301d47d2773830687f0fdaaa8b263914564c527d9",
        "2c86680ddd0725e9b2af495ee35323448857e92d6400d84dfe3eb6cbff09d982",
        "20580670c6aee21bf2939ab1e75f321bc770326571151ee1b971461b1a485d34",
        "19d278981137c795751250ada37ff5f6967df47c1924fd0c01eaf73f3755dee2",
        "284d344ac35e17eda12715cab736a7bf80985220618e1982d0ba87f483e29548",
        "10d804047e9456a88e30ce550825ec9de169a8c8c294b8ad7d7d9c9de862d959",
        "1f28bad964382258926d40448c4a52bb012b79baca651fe9caa46dcddb4c692e",
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        "2bc0654015030b29571086241ab881d5bab80d589a922cb896f0c7962c07d509",
        "1ba66d34c3a034efbffdbc70788baff1a5c2c6947d3d2e39f20e067e61dd30a5",
        "171c6eb8e3b7feeb8ffc180d36f3feba07568c920a4485bb48494ff5261ebd88",
        "000f2aa6f3c58ced4f2f0c538a3fb177d78805ae1288aa3cf066d877b2401977",
        "199c3394332b5cf6cc76a7ebe77610044b332aecb42a1771edbd65104833f4af",
        "10513888b62572e6acf4147465bf4a7ac6416dd48eb03c49b13a4b4332e18c4c",
        "14267072085228373a584741bb0bdc84b2eadf76b3943431f964f56de37db0db",
        "0bd0afc8b66c76e1a9c3f1df18dec78cfd4d5915eff635f4684fd17f740efd67",
        "07a1ede5b2a43711f9d1590fb40adb80cf66de2d6890a230c8f7d51a06af2c39",
        "25e69119f1a08617ab204097e820f82e9a05606680abba0fde0db81e1fd0bad3",
        "2f52c04cd7657c69c53a1007cae1388b105945bc81071e79a8f278b498972a28",
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        "2eddf87dabd2df616e6afcadb6c1dce2c0dcd074d9eb44dd3a670f9b5e081106",
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        "0c9462aee892e3b878c67bf9c0a99a0a7dd0302a807bffd347cd76a48106bfe9",
        "0d447987f491bf61f15fc0a9f909919a93b2210d624195293fd600a2c9266fe8",
        "0e3dadc74b8817b2b4cb32a78a6c910060e5a4cd79cbfd6a1146069a87e420a7",
        "278c0bc5addb7303cff9b3570df6176493de54f43f15aae2416d9bc170957333",
        "17dfe0688d2afde487cae0e14a01f02384e7b5c61a659c8bf4df4f36cbf6012c",
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        "1462aafe0e864b2e54e7d62c594059b464ba9a3e4a3a220e28b22bc598d1df83",
        "1d52e0faf9391bc44ba1f66fe637e8e95dde8e7eee9491f9471aa8aae5ed133e",
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        "133d1b51829583b18d2afaa251686a4148f8ca24dce3fc378ba9ddc1a3d66a4c",
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        "08c5195b776aab95da6ca17eac81849df8785af3373526ae6a76e7fa4fe95673",
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        "0d454faa86f40794dd02f256c1a338c22f3c814c847b4e205cf20082ff1a5827",
        "287e7a4cea0baa17d1c3132536df29f057d03abf655feda515cee4bd45001de8",
        "1658219d6a2fddc4251f3432bbc8b9e49684fcd79aae97a0e78df0104d060ff0",
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        "251fba7c2bccc579147461d7caed44ffc4d7aba749f7c480a143fcc52ff6d0d4",
        "0f88bd8cbf293e53bd7ea661309647621bf243b07c3010867a71e81d56daa32e",
        "2e50739ded1d40ef1faffa7247fb35f3f3d8738bb300053009720f464b245b4a",
        "08a860efa3e963177cd69cd935fd4ce61812deb1ef476eba5c18b53a1825f73d",
        "02ef0b5bfd2869670ddc1dde1c9a29ac9a93a28633dd55cd543dd93d031a3776",
        "00ad678ff09f4f1d62f3eb67a93e95202c4002b4435a3930b2e97fc8a437c860",
        "2c53a9ac608631a119e7f57ed5cb0498134671e6f517757546b3ff61dc24ea9d",
        "0b262e363290fd3157aa34482f7d3b63e7293e766a34c528fcaeac7b78c669ab",
        "2c729367130f7492d6c7fa81d933e572ceb2cae48abff54290364f7ffd98bbe2",
        "0c52b752688f7c1231a81213da5d399f0de08127a0410ab6cec26224520a7302",
        "015ed07c528f1f75c39013233daae79023c9a10051e272b2a0a5596745b50def",
        "054c68de3da880b3efd04d6dd592070402cd24056b7c170657335e9ccfb45ed9",
        "0653a2625249ca142027b136af44aa3bea7ce98801ab7964102b20385ed3e38f",
        "128265fbcf4f8dc26f44e5de2ccbd57ac858b7a1a3d955a1cafe98de79d239ef",
        "290a90817d105423426ab71c2b097df309086c3cc0b83ccb1bf90486cbce4114",
        "0ec81adacd88f9f1401c42ceb56348bbf36181a0c03f2512e34fdef39f23859b",
        "0059843dff350356ce8db94fc588542dcd43c7621d326a56c7de9126548a84ef",
        "05f1d7d0fc3a5e6bfc55ce75e7688236e879a7f60cb52f138f52069b048f05a9",
        "2dadc5fa46bbc50df63dadfc9b4fa72bd344e26e93f0fbc184f03bf4a76b51e1",
        "1bf5f44265a2400afe65e220ed0c8b49306770e192cfcbe06c8c28206a42cd78",
        "0f484d2249c289e95f4c1b2fa0330572037b157ae41187aebf92468d617dacd5",
        "1a4dd8999a4847cb26d5cc32ac2b94ff7f5e4e6a37263e34cb18dd53d8be1b75",
        "2fbf545602120abfff0a56316d9143d152d43816ef782a67780e1b8f9252a4ff",
        "1835d89422d3d824fad14501a3f3c8a6ae474df2b5a29011b5c36030c2b8bdfe",
        "18c215d302d89a958d8d9cdad60b5010024e91b510bcab7ffbb384cd21b625da",
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        "2a79af347cb1fa3996755c7f68ad83f86b86ba81bd2b9fa98948cfcef63cce23",
        "0c38e0161d3e3d317108e518dc74150f8205fb74083fd47b3b88aafc9d0130cf",
        "0d65129efa0b7fe99f91e540166753bbbff12cdaa9b5777208f26ba72a87b52a",
        "065923e0aa248690099aa247581f481061d9243cedec15a538c6f3dabc54ed3f",
        "209749a7661b281882cd713683824ed6122820968a9552ed27f208a45c2837ec",
        "0567e0493586c14d0ef128252f9a20c74602ec56626b5c2f3644fc79a7983a16",
        "2a3746ab2d1fd023c90559abcb8c36d3273b3685b7da3332b3162e894a6cbcea",
        "2fe83a4aa399397b998bc1bf32a322b69e58244d60ccfb546c013ec9818e1355",
        "2cba41b38555075f0caa9773c8f358d018620c4fec64c15142e33bae27ff07be",
        "262d890f3c3d9ebe6eb150754a0677d94a64f645ddc813eb87f82418160376bc",
        "184043dc9ed8d23817f34010c7689116620fb892ebe7b92e7afeb2dff8203bb0",
        "16150e6cd627f1aab252d573c715c3e132d63d714e232c200a86db5279dc24f9",
        "1aa1be02875b4dd93beaa0841dc74dd43b2f69accd3c3625cd28e720fc3077be",
        "0870eb40106c6c25725f4e303741257e730098d7d4f7c07155bc89c805f3e573",
        "2c174e5eaedc48a0f83b0638038d79d5ce719a7ba41a974f68dc307a4d7df27e",
        "1c5f8c2978c5db3c6483e6c59ecfa4b4591f81c346f882166fe1395f09067c01",
        "25a5229df981407d38b35494facd5d3be74835427a084bc796046ee533804256",
        "14198c56049b0bafe24c1e58227a15dfdc1730f7570a0425cc3f5175078d3b46",
        "06f649866a0de8a7127623c9a87e528dea9d7df9a761fd1bbce65bc1dccc06aa",
        "1164c0172f7edcf878d89bec7c593dbac32f366f7c26136c219c9ff79fb4ba8f",
        "1d57c7d112c7559eef860394ffa55686dc4addc269e1f4763a3a329d85b9203c",
        "29c8787c8830fac709c646dbfda04db6ecf9f508e056fb42d9a7efd3bb0a0360",
        "23ef9d9c4a48657f835f302dd6f6efa94f21f7d65fd188fe53c540bc7fbb48f2",
        "259ff75fdd8a23943f9d9e91e335395223a11bde135182fc543af4763a9c491b",
        "1b14061e2f2c468feb62b9ce08729d60a700aad2f37e7aefdcd977243a50f02f",
        "2a79870f9070251178edd6c30596db17a75375b7bc163d39cfa97f42bea1e487",
        "2920015344e43aa0e279bb8bbd180ad00f80a2d88d7ee3d75f794ea94f788c5c",
        "262f785087e1fb1873a803e55d7f1b6e1d31ae6ce6c25ad0a1ce39f3dc870765",
        "2f34183f18efd7f36cf92ef3310ea2b5fcbdc68a08ec1246f86ec7821bdd3593",
        "24976ddc28c17b43f06aff004f5237fdf5216bcc98656c4cbfd80d2ceb28f5b4",
        "1c75ba32a127cae227f83616357be97ccf95559f4e10a202f6f073f6615708a2",
        "29a2d25cbda9f5b67fa860e6d42bd3408a8538b9c6879851db68d2a6bcafc02d",
        "0aa84212e380e99137636932c0aadb021c2ecd448bfde7f9bba46dbfae9847c5",
        "21f78689e3e2585bd2fa23848df576d8ca6a20c1e22ad912ba5e9bd9317f072c",
        "293a1159d1c02a6429adbb0da020a819a687ee7047679c3c60d58c3ff98ae3ea",
        "1a7d485f430c376e12fc7d1b3613a511822193599e15e0b30d214cb989edd72d",
        "148f89c16be581d1dde28de8b229a14509505effd37e672e3f47a90515f0767d",
        "03c2411a03c742bb60b08116a2fd8ea86e1cbaa1f6f82b45951801caab0a6448",
        "05b054684c6e494317541efe51da10ca76fb31a10452b442e4993814a08b6bf1",
        "1ca534bb0ce1f2ae8149ababf167c5491f00edb4b144f6ea92a7d7918b6d4cd3",
        "1c2740412825060b5f2a80d387fd83d5023d1be26ba6eb2b0a5d8e90ecf98f44",
        "15832c8f5667b380e31a84435232af18e685d784d201faf7b9bbae68c20aca82",
        "14d6fefe0a848db15e0baddc508b71614642dc5dca6e267a4c082eedb7f22f3e",
        "0c0a1384c660a036ad581bcce6af24ca06f7b647be7fea648cef6355901fadb1",
        "24d5243e9dfd338ac19c7a01a6edb2ddfafb256e6b84964d3c50cb3fd8dca48e",
        "0a4d7c32d85fe6458c9b48597aa03087ff6ad9a766ae6e3db65e2b23b6d7dd52",
        "1db213ff1511c1dbd7f764afcafb3d1ac5811e7a5795fe61f00ab8abad903bdd",
        "1665a557b4a74548ceec6f598ab5684f32bcaa867c12e8d1abdd6acee1285792",
        "2fd5d39615c3cfbe8ccc5e362e635cfe06c588e9bc0cb1d95c1df71dad1c0b7d",
        "100e6f9483e9c38ce0a7fe26cfd8bd1d915a967ef85e9c3126b6f97b8c67ab0f",
        "02f04bc9ea7e55f3901d844e427bc348f934f48551eb0b60051f9ee756a6aa3c",
        "18bf6a3dc3320590adae58baf410b4367785d21d0a38e1fd8ad0b5ac73ecf609"
    ];

    let mut acc = Fr::one();
    for i in 0..10000 {
        assert!(expected[i] == into_hex(acc).unwrap());
        assert!(from_hex::<Fr>(expected[i]).unwrap() == acc);

        acc = acc * acc + acc + acc.inverse().unwrap();
    }
}