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halo2/halo2_proofs/tests/plonk_api.rs

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#![allow(clippy::many_single_char_names)]
#![allow(clippy::op_ref)]
use assert_matches::assert_matches;
use group::ff::{Field, WithSmallOrderMulGroup};
use halo2_proofs::arithmetic::CurveAffine;
use halo2_proofs::circuit::{Cell, Layouter, SimpleFloorPlanner, Value};
use halo2_proofs::dev::MockProver;
use halo2_proofs::pasta::{Eq, EqAffine, Fp};
use halo2_proofs::plonk::{
create_proof, keygen_pk, keygen_vk, verify_proof, Advice, Assigned, BatchVerifier, Circuit,
Column, ConstraintSystem, Error, Fixed, SingleVerifier, TableColumn, VerificationStrategy,
};
use halo2_proofs::poly::commitment::{Guard, MSM};
use halo2_proofs::poly::{commitment::Params, Rotation};
use halo2_proofs::transcript::{Blake2bRead, Blake2bWrite, Challenge255, EncodedChallenge};
use rand_core::OsRng;
use std::marker::PhantomData;
#[test]
fn plonk_api() {
const K: u32 = 5;
/// This represents an advice column at a certain row in the ConstraintSystem
#[derive(Copy, Clone, Debug)]
pub struct Variable(Column<Advice>, usize);
// Initialize the polynomial commitment parameters
let params: Params<EqAffine> = Params::new(K);
#[derive(Clone)]
struct PlonkConfig {
a: Column<Advice>,
b: Column<Advice>,
c: Column<Advice>,
d: Column<Advice>,
e: Column<Advice>,
sa: Column<Fixed>,
sb: Column<Fixed>,
sc: Column<Fixed>,
sm: Column<Fixed>,
sp: Column<Fixed>,
sl: TableColumn,
}
#[allow(clippy::type_complexity)]
trait StandardCs<FF: Field> {
fn raw_multiply<F>(
&self,
layouter: &mut impl Layouter<FF>,
f: F,
) -> Result<(Cell, Cell, Cell), Error>
where
F: FnMut() -> Value<(Assigned<FF>, Assigned<FF>, Assigned<FF>)>;
fn raw_add<F>(
&self,
layouter: &mut impl Layouter<FF>,
f: F,
) -> Result<(Cell, Cell, Cell), Error>
where
F: FnMut() -> Value<(Assigned<FF>, Assigned<FF>, Assigned<FF>)>;
fn copy(&self, layouter: &mut impl Layouter<FF>, a: Cell, b: Cell) -> Result<(), Error>;
fn public_input<F>(&self, layouter: &mut impl Layouter<FF>, f: F) -> Result<Cell, Error>
where
F: FnMut() -> Value<FF>;
fn lookup_table(
&self,
layouter: &mut impl Layouter<FF>,
values: &[FF],
) -> Result<(), Error>;
}
#[derive(Clone)]
struct MyCircuit<F: Field> {
a: Value<F>,
lookup_table: Vec<F>,
}
struct StandardPlonk<F: Field> {
config: PlonkConfig,
_marker: PhantomData<F>,
}
impl<FF: Field> StandardPlonk<FF> {
fn new(config: PlonkConfig) -> Self {
StandardPlonk {
config,
_marker: PhantomData,
}
}
}
impl<FF: Field> StandardCs<FF> for StandardPlonk<FF> {
fn raw_multiply<F>(
&self,
layouter: &mut impl Layouter<FF>,
mut f: F,
) -> Result<(Cell, Cell, Cell), Error>
where
F: FnMut() -> Value<(Assigned<FF>, Assigned<FF>, Assigned<FF>)>,
{
layouter.assign_region(
|| "raw_multiply",
|mut region| {
let mut value = None;
let lhs = region.assign_advice(
|| "lhs",
self.config.a,
0,
|| {
value = Some(f());
value.unwrap().map(|v| v.0)
},
)?;
region.assign_advice(
|| "lhs^4",
self.config.d,
0,
|| value.unwrap().map(|v| v.0).square().square(),
)?;
let rhs = region.assign_advice(
|| "rhs",
self.config.b,
0,
|| value.unwrap().map(|v| v.1),
)?;
region.assign_advice(
|| "rhs^4",
self.config.e,
0,
|| value.unwrap().map(|v| v.1).square().square(),
)?;
let out = region.assign_advice(
|| "out",
self.config.c,
0,
|| value.unwrap().map(|v| v.2),
)?;
region.assign_fixed(|| "a", self.config.sa, 0, || Value::known(FF::ZERO))?;
region.assign_fixed(|| "b", self.config.sb, 0, || Value::known(FF::ZERO))?;
region.assign_fixed(|| "c", self.config.sc, 0, || Value::known(FF::ONE))?;
region.assign_fixed(|| "a * b", self.config.sm, 0, || Value::known(FF::ONE))?;
Ok((lhs.cell(), rhs.cell(), out.cell()))
},
)
}
fn raw_add<F>(
&self,
layouter: &mut impl Layouter<FF>,
mut f: F,
) -> Result<(Cell, Cell, Cell), Error>
where
F: FnMut() -> Value<(Assigned<FF>, Assigned<FF>, Assigned<FF>)>,
{
layouter.assign_region(
|| "raw_add",
|mut region| {
let mut value = None;
let lhs = region.assign_advice(
|| "lhs",
self.config.a,
0,
|| {
value = Some(f());
value.unwrap().map(|v| v.0)
},
)?;
region.assign_advice(
|| "lhs^4",
self.config.d,
0,
|| value.unwrap().map(|v| v.0).square().square(),
)?;
let rhs = region.assign_advice(
|| "rhs",
self.config.b,
0,
|| value.unwrap().map(|v| v.1),
)?;
region.assign_advice(
|| "rhs^4",
self.config.e,
0,
|| value.unwrap().map(|v| v.1).square().square(),
)?;
let out = region.assign_advice(
|| "out",
self.config.c,
0,
|| value.unwrap().map(|v| v.2),
)?;
region.assign_fixed(|| "a", self.config.sa, 0, || Value::known(FF::ONE))?;
region.assign_fixed(|| "b", self.config.sb, 0, || Value::known(FF::ONE))?;
region.assign_fixed(|| "c", self.config.sc, 0, || Value::known(FF::ONE))?;
region.assign_fixed(
|| "a * b",
self.config.sm,
0,
|| Value::known(FF::ZERO),
)?;
Ok((lhs.cell(), rhs.cell(), out.cell()))
},
)
}
fn copy(
&self,
layouter: &mut impl Layouter<FF>,
left: Cell,
right: Cell,
) -> Result<(), Error> {
layouter.assign_region(
|| "copy",
|mut region| {
region.constrain_equal(left, right)?;
region.constrain_equal(left, right)
},
)
}
fn public_input<F>(&self, layouter: &mut impl Layouter<FF>, mut f: F) -> Result<Cell, Error>
where
F: FnMut() -> Value<FF>,
{
layouter.assign_region(
|| "public_input",
|mut region| {
let value = region.assign_advice(|| "value", self.config.a, 0, &mut f)?;
region.assign_fixed(
|| "public",
self.config.sp,
0,
|| Value::known(FF::ONE),
)?;
Ok(value.cell())
},
)
}
fn lookup_table(
&self,
layouter: &mut impl Layouter<FF>,
values: &[FF],
) -> Result<(), Error> {
layouter.assign_table(
|| "",
|mut table| {
for (index, &value) in values.iter().enumerate() {
table.assign_cell(
|| "table col",
self.config.sl,
index,
|| Value::known(value),
)?;
}
Ok(())
},
)?;
Ok(())
}
}
impl<F: Field> Circuit<F> for MyCircuit<F> {
type Config = PlonkConfig;
type FloorPlanner = SimpleFloorPlanner;
fn without_witnesses(&self) -> Self {
Self {
a: Value::unknown(),
lookup_table: self.lookup_table.clone(),
}
}
fn configure(meta: &mut ConstraintSystem<F>) -> PlonkConfig {
let e = meta.advice_column();
let a = meta.advice_column();
let b = meta.advice_column();
let sf = meta.fixed_column();
let c = meta.advice_column();
let d = meta.advice_column();
let p = meta.instance_column();
meta.enable_equality(a);
meta.enable_equality(b);
meta.enable_equality(c);
let sm = meta.fixed_column();
let sa = meta.fixed_column();
let sb = meta.fixed_column();
let sc = meta.fixed_column();
let sp = meta.fixed_column();
let sl = meta.lookup_table_column();
/*
* A B ... sl
* [
* instance 0 ... 0
* a a ... 0
* a a^2 ... 0
* a a ... 0
* a a^2 ... 0
* ... ... ... ...
* ... ... ... instance
* ... ... ... a
* ... ... ... a
* ... ... ... 0
* ]
*/
meta.lookup(|meta| {
let a_ = meta.query_any(a, Rotation::cur());
vec![(a_, sl)]
});
meta.create_gate("Combined add-mult", |meta| {
let d = meta.query_advice(d, Rotation::next());
let a = meta.query_advice(a, Rotation::cur());
let sf = meta.query_fixed(sf);
let e = meta.query_advice(e, Rotation::prev());
let b = meta.query_advice(b, Rotation::cur());
let c = meta.query_advice(c, Rotation::cur());
let sa = meta.query_fixed(sa);
let sb = meta.query_fixed(sb);
let sc = meta.query_fixed(sc);
let sm = meta.query_fixed(sm);
vec![a.clone() * sa + b.clone() * sb + a * b * sm - (c * sc) + sf * (d * e)]
});
meta.create_gate("Public input", |meta| {
let a = meta.query_advice(a, Rotation::cur());
let p = meta.query_instance(p, Rotation::cur());
let sp = meta.query_fixed(sp);
vec![sp * (a - p)]
});
meta.enable_equality(sf);
meta.enable_equality(e);
meta.enable_equality(d);
meta.enable_equality(p);
meta.enable_equality(sm);
meta.enable_equality(sa);
meta.enable_equality(sb);
meta.enable_equality(sc);
meta.enable_equality(sp);
PlonkConfig {
a,
b,
c,
d,
e,
sa,
sb,
sc,
sm,
sp,
sl,
}
}
fn synthesize(
&self,
config: PlonkConfig,
mut layouter: impl Layouter<F>,
) -> Result<(), Error> {
let cs = StandardPlonk::new(config);
let _ = cs.public_input(&mut layouter, || Value::known(F::ONE + F::ONE))?;
for _ in 0..10 {
let a: Value<Assigned<_>> = self.a.into();
let mut a_squared = Value::unknown();
let (a0, _, c0) = cs.raw_multiply(&mut layouter, || {
a_squared = a.square();
a.zip(a_squared).map(|(a, a_squared)| (a, a, a_squared))
})?;
let (a1, b1, _) = cs.raw_add(&mut layouter, || {
let fin = a_squared + a;
a.zip(a_squared)
.zip(fin)
.map(|((a, a_squared), fin)| (a, a_squared, fin))
})?;
cs.copy(&mut layouter, a0, a1)?;
cs.copy(&mut layouter, b1, c0)?;
}
cs.lookup_table(&mut layouter, &self.lookup_table)?;
Ok(())
}
}
let a = Fp::from(2834758237) * Fp::ZETA;
let instance = Fp::ONE + Fp::ONE;
let lookup_table = vec![instance, a, a, Fp::ZERO];
let empty_circuit: MyCircuit<Fp> = MyCircuit {
a: Value::unknown(),
lookup_table: lookup_table.clone(),
};
let circuit: MyCircuit<Fp> = MyCircuit {
a: Value::known(a),
lookup_table,
};
// Check that we get an error if we try to initialize the proving key with a value of
// k that is too small for the minimum required number of rows.
let much_too_small_params: Params<EqAffine> = Params::new(1);
assert_matches!(
keygen_vk(&much_too_small_params, &empty_circuit),
Err(Error::NotEnoughRowsAvailable {
current_k,
}) if current_k == 1
);
// Check that we get an error if we try to initialize the proving key with a value of
// k that is too small for the number of rows the circuit uses.
let slightly_too_small_params: Params<EqAffine> = Params::new(K - 1);
assert_matches!(
keygen_vk(&slightly_too_small_params, &empty_circuit),
Err(Error::NotEnoughRowsAvailable {
current_k,
}) if current_k == K - 1
);
// Initialize the proving key
let vk = keygen_vk(&params, &empty_circuit).expect("keygen_vk should not fail");
let pk = keygen_pk(&params, vk, &empty_circuit).expect("keygen_pk should not fail");
let pubinputs = vec![instance];
// Check this circuit is satisfied.
let prover = match MockProver::run(K, &circuit, vec![pubinputs.clone()]) {
Ok(prover) => prover,
Err(e) => panic!("{:?}", e),
};
assert_eq!(prover.verify(), Ok(()));
if std::env::var_os("HALO2_PLONK_TEST_GENERATE_NEW_PROOF").is_some() {
let mut transcript = Blake2bWrite::<_, _, Challenge255<_>>::init(vec![]);
// Create a proof
create_proof(
&params,
&pk,
&[circuit.clone(), circuit.clone()],
&[&[&[instance]], &[&[instance]]],
OsRng,
&mut transcript,
)
.expect("proof generation should not fail");
let proof: Vec<u8> = transcript.finalize();
std::fs::write("./tests/plonk_api_proof.bin", &proof[..])
.expect("should succeed to write new proof");
}
{
// Check that a hardcoded proof is satisfied
let proof =
std::fs::read("./tests/plonk_api_proof.bin").expect("should succeed to read proof");
let strategy = SingleVerifier::new(&params);
let mut transcript = Blake2bRead::<_, _, Challenge255<_>>::init(&proof[..]);
assert!(verify_proof(
&params,
pk.get_vk(),
strategy,
&[&[&pubinputs[..]], &[&pubinputs[..]]],
&mut transcript,
)
.is_ok());
}
for _ in 0..10 {
let mut transcript = Blake2bWrite::<_, _, Challenge255<_>>::init(vec![]);
// Create a proof
create_proof(
&params,
&pk,
&[circuit.clone(), circuit.clone()],
&[&[&[instance]], &[&[instance]]],
OsRng,
&mut transcript,
)
.expect("proof generation should not fail");
let proof: Vec<u8> = transcript.finalize();
assert_eq!(
proof.len(),
halo2_proofs::dev::CircuitCost::<Eq, MyCircuit<_>>::measure(K, &circuit)
.proof_size(2)
.into(),
);
// Test single-verifier strategy.
{
let strategy = SingleVerifier::new(&params);
let mut transcript = Blake2bRead::<_, _, Challenge255<_>>::init(&proof[..]);
assert!(verify_proof(
&params,
pk.get_vk(),
strategy,
&[&[&pubinputs[..]], &[&pubinputs[..]]],
&mut transcript,
)
.is_ok());
}
//
// Test accumulation-based strategy.
//
struct AccumulationVerifier<'params, C: CurveAffine> {
msm: MSM<'params, C>,
}
impl<'params, C: CurveAffine> AccumulationVerifier<'params, C> {
fn new(params: &'params Params<C>) -> Self {
AccumulationVerifier {
msm: MSM::new(params),
}
}
}
impl<'params, C: CurveAffine> VerificationStrategy<'params, C>
for AccumulationVerifier<'params, C>
{
type Output = ();
fn process<E: EncodedChallenge<C>>(
self,
f: impl FnOnce(MSM<'params, C>) -> Result<Guard<'params, C, E>, Error>,
) -> Result<Self::Output, Error> {
let guard = f(self.msm)?;
let g = guard.compute_g();
let (msm, _) = guard.use_g(g);
if msm.eval() {
Ok(())
} else {
Err(Error::ConstraintSystemFailure)
}
}
}
{
let strategy = AccumulationVerifier::new(&params);
let mut transcript = Blake2bRead::<_, _, Challenge255<_>>::init(&proof[..]);
assert!(verify_proof(
&params,
pk.get_vk(),
strategy,
&[&[&pubinputs[..]], &[&pubinputs[..]]],
&mut transcript,
)
.is_ok());
}
//
// Test batch-verifier strategy.
//
{
let mut batch = BatchVerifier::new();
// First proof.
batch.add_proof(
vec![vec![pubinputs.clone()], vec![pubinputs.clone()]],
proof.clone(),
);
// "Second" proof (just the first proof again).
batch.add_proof(
vec![vec![pubinputs.clone()], vec![pubinputs.clone()]],
proof,
);
// Check the batch.
assert!(batch.finalize(&params, pk.get_vk()));
}
}
// Check that the verification key has not changed unexpectedly
{
//panic!("{:#?}", pk.get_vk().pinned());
assert_eq!(
format!("{:#?}", pk.get_vk().pinned()),
r#####"PinnedVerificationKey {
base_modulus: "0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001",
scalar_modulus: "0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001",
domain: PinnedEvaluationDomain {
k: 5,
extended_k: 7,
omega: 0x0cc3380dc616f2e1daf29ad1560833ed3baea3393eceb7bc8fa36376929b78cc,
},
cs: PinnedConstraintSystem {
num_fixed_columns: 7,
num_advice_columns: 5,
num_instance_columns: 1,
num_selectors: 0,
gates: [
Sum(
Sum(
Sum(
Sum(
Product(
Advice {
query_index: 0,
column_index: 1,
rotation: Rotation(
0,
),
},
Fixed {
query_index: 2,
column_index: 2,
rotation: Rotation(
0,
),
},
),
Product(
Advice {
query_index: 1,
column_index: 2,
rotation: Rotation(
0,
),
},
Fixed {
query_index: 3,
column_index: 3,
rotation: Rotation(
0,
),
},
),
),
Product(
Product(
Advice {
query_index: 0,
column_index: 1,
rotation: Rotation(
0,
),
},
Advice {
query_index: 1,
column_index: 2,
rotation: Rotation(
0,
),
},
),
Fixed {
query_index: 5,
column_index: 1,
rotation: Rotation(
0,
),
},
),
),
Negated(
Product(
Advice {
query_index: 2,
column_index: 3,
rotation: Rotation(
0,
),
},
Fixed {
query_index: 4,
column_index: 4,
rotation: Rotation(
0,
),
},
),
),
),
Product(
Fixed {
query_index: 1,
column_index: 0,
rotation: Rotation(
0,
),
},
Product(
Advice {
query_index: 3,
column_index: 4,
rotation: Rotation(
1,
),
},
Advice {
query_index: 4,
column_index: 0,
rotation: Rotation(
-1,
),
},
),
),
),
Product(
Fixed {
query_index: 6,
column_index: 5,
rotation: Rotation(
0,
),
},
Sum(
Advice {
query_index: 0,
column_index: 1,
rotation: Rotation(
0,
),
},
Negated(
Instance {
query_index: 0,
column_index: 0,
rotation: Rotation(
0,
),
},
),
),
),
],
advice_queries: [
(
Column {
index: 1,
column_type: Advice,
},
Rotation(
0,
),
),
(
Column {
index: 2,
column_type: Advice,
},
Rotation(
0,
),
),
(
Column {
index: 3,
column_type: Advice,
},
Rotation(
0,
),
),
(
Column {
index: 4,
column_type: Advice,
},
Rotation(
1,
),
),
(
Column {
index: 0,
column_type: Advice,
},
Rotation(
-1,
),
),
(
Column {
index: 0,
column_type: Advice,
},
Rotation(
0,
),
),
(
Column {
index: 4,
column_type: Advice,
},
Rotation(
0,
),
),
],
instance_queries: [
(
Column {
index: 0,
column_type: Instance,
},
Rotation(
0,
),
),
],
fixed_queries: [
(
Column {
index: 6,
column_type: Fixed,
},
Rotation(
0,
),
),
(
Column {
index: 0,
column_type: Fixed,
},
Rotation(
0,
),
),
(
Column {
index: 2,
column_type: Fixed,
},
Rotation(
0,
),
),
(
Column {
index: 3,
column_type: Fixed,
},
Rotation(
0,
),
),
(
Column {
index: 4,
column_type: Fixed,
},
Rotation(
0,
),
),
(
Column {
index: 1,
column_type: Fixed,
},
Rotation(
0,
),
),
(
Column {
index: 5,
column_type: Fixed,
},
Rotation(
0,
),
),
],
permutation: Argument {
columns: [
Column {
index: 1,
column_type: Advice,
},
Column {
index: 2,
column_type: Advice,
},
Column {
index: 3,
column_type: Advice,
},
Column {
index: 0,
column_type: Fixed,
},
Column {
index: 0,
column_type: Advice,
},
Column {
index: 4,
column_type: Advice,
},
Column {
index: 0,
column_type: Instance,
},
Column {
index: 1,
column_type: Fixed,
},
Column {
index: 2,
column_type: Fixed,
},
Column {
index: 3,
column_type: Fixed,
},
Column {
index: 4,
column_type: Fixed,
},
Column {
index: 5,
column_type: Fixed,
},
],
},
lookups: [
Argument {
input_expressions: [
Advice {
query_index: 0,
column_index: 1,
rotation: Rotation(
0,
),
},
],
table_expressions: [
Fixed {
query_index: 0,
column_index: 6,
rotation: Rotation(
0,
),
},
],
},
],
constants: [],
minimum_degree: None,
},
fixed_commitments: [
(0x2bbc94ef7b22aebef24f9a4b0cc1831882548b605171366017d45c3e6fd92075, 0x082b801a6e176239943bfb759fb02138f47a5c8cc4aa7fa0af559fde4e3abd97),
(0x2bf5082b105b2156ed0e9c5b8e42bf2a240b058f74a464d080e9585274dd1e84, 0x222ad83cee7777e7a160585e212140e5e770dd8d1df788d869b5ee483a5864fb),
(0x374a656456a0aae7429b23336f825752b575dd5a44290ff614946ee59d6a20c0, 0x054491e187e6e3460e7601fb54ae10836d34d420026f96316f0c5c62f86db9b8),
(0x374a656456a0aae7429b23336f825752b575dd5a44290ff614946ee59d6a20c0, 0x054491e187e6e3460e7601fb54ae10836d34d420026f96316f0c5c62f86db9b8),
(0x02e62cd68370b13711139a08cbcdd889e800a272b9ea10acc90880fff9d89199, 0x1a96c468cb0ce77065d3a58f1e55fea9b72d15e44c01bba1e110bd0cbc6e9bc6),
(0x224ef42758215157d3ee48fb8d769da5bddd35e5929a90a4a89736f5c4b5ae9b, 0x11bc3a1e08eb320cde764f1492ecef956d71e996e2165f7a9a30ad2febb511c1),
(0x2d5415bf917fcac32bfb705f8ca35cb12d9bad52aa33ccca747350f9235d3a18, 0x2b2921f815fad504052512743963ef20ed5b401d20627793b006413e73fe4dd4),
],
permutation: VerifyingKey {
commitments: [
(0x1347b4b385837977a96b87f199c6a9a81520015539d1e8fa79429bb4ca229a00, 0x2168e404cabef513654d6ff516cde73f0ba87e3dc84e4b940ed675b5f66f3884),
(0x0e6d69cd2455ec43be640f6397ed65c9e51b1d8c0fd2216339314ff37ade122a, 0x222ed6dc8cfc9ea26dcc10b9d4add791ada60f2b5a63ee1e4635f88aa0c96654),
(0x13c447846f48c41a5e0675ccf88ebc0cdef2c96c51446d037acb866d24255785, 0x1f0b5414fc5e8219dbfab996eed6129d831488b2386a8b1a63663938903bd63a),
(0x1aae6470aa662b8fda003894ddef5fedd03af318b3231683039d2fac9cab05b9, 0x08832d91ae69e99cd07d096c7a4a284a69e6a16227cbb07932a0cdc56914f3a6),
(0x0850521b0f8ac7dd0550fe3e25c840837076e9635067ed623b81d5cbac5944d9, 0x0c25d65d1038d0a92c72e5fccd96c1caf07801c3c8233290bb292e0c38c256fa),
(0x12febcf696badd970750eabf75dd3ced4c2f54f93519bcee23849025177d2014, 0x0a05ab3cd42c9fbcc1bbfcf9269951640cc9920761c87cf8e211ba73c8d9f90f),
(0x053904bdde8cfead3b517bb4f6ded3e699f8b94ca6156a9dd2f92a2a05a7ec5a, 0x16753ff97c0d82ff586bb7a07bf7f27a92df90b3617fa5e75d4f55c3b0ef8711),
(0x3804548f6816452747a5b542fa5656353fc989db40d69e9e27d6f973b5deebb0, 0x389a44d5037866dd83993af75831a5f90a18ad5244255aa5bd2c922cc5853055),
(0x003a9f9ca71c7c0b832c802220915f6fc8d840162bdde6b0ea05d25fb95559e3, 0x091247ca19d6b73887cd7f68908cbf0db0b47459b7c82276bbdb8a1c937e2438),
(0x3eaa38689d9e391c8a8fafab9568f20c45816321d38f309d4cc37f4b1601af72, 0x247f8270a462ea88450221a56aa6b55d2bc352b80b03501e99ea983251ceea13),
(0x394437571f9de32dccdc546fd4737772d8d92593c85438aa3473243997d5acc8, 0x14924ec6e3174f1fab7f0ce7070c22f04bbd0a0ecebdfc5c94be857f25493e95),
(0x3d907e0591343bd285c2c846f3e871a6ac70d80ec29e9500b8cb57f544e60202, 0x1034e48df35830244cabea076be8a16d67d7896e27c6ac22b285d017105da9c3),
],
},
}"#####
);
}
}
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