mirror of
https://github.com/kaspanet/kaspad.git
synced 2025-03-30 15:08:33 +00:00
6afc06ce58
* Replace p2pkh with p2pk * Fix tests * Fix comments and variable names * Add README.md for genkeypair * Rename pubkey->publicKey * Rename p2pkh to p2pk * Use util.PublicKeySize where needed * Remove redundant pointer * Fix comment * Rename pubKey->publicKey
395 lines
17 KiB
Go
395 lines
17 KiB
Go
package consensushashing_test
|
|
|
|
import (
|
|
"encoding/hex"
|
|
"fmt"
|
|
"testing"
|
|
|
|
"github.com/kaspanet/go-secp256k1"
|
|
|
|
"github.com/kaspanet/kaspad/domain/consensus/utils/consensushashing"
|
|
"github.com/kaspanet/kaspad/domain/consensus/utils/txscript"
|
|
"github.com/kaspanet/kaspad/domain/consensus/utils/utxo"
|
|
"github.com/kaspanet/kaspad/domain/dagconfig"
|
|
"github.com/kaspanet/kaspad/util"
|
|
|
|
"github.com/kaspanet/kaspad/domain/consensus/model/externalapi"
|
|
)
|
|
|
|
// shortened versions of SigHash types to fit in single line of test case
|
|
const (
|
|
all = consensushashing.SigHashAll
|
|
none = consensushashing.SigHashNone
|
|
single = consensushashing.SigHashSingle
|
|
allAnyoneCanPay = consensushashing.SigHashAll | consensushashing.SigHashAnyOneCanPay
|
|
noneAnyoneCanPay = consensushashing.SigHashNone | consensushashing.SigHashAnyOneCanPay
|
|
singleAnyoneCanPay = consensushashing.SigHashSingle | consensushashing.SigHashAnyOneCanPay
|
|
)
|
|
|
|
func modifyOutput(outputIndex int) func(tx *externalapi.DomainTransaction) *externalapi.DomainTransaction {
|
|
return func(tx *externalapi.DomainTransaction) *externalapi.DomainTransaction {
|
|
clone := tx.Clone()
|
|
clone.Outputs[outputIndex].Value = 100
|
|
return clone
|
|
}
|
|
}
|
|
|
|
func modifyInput(inputIndex int) func(tx *externalapi.DomainTransaction) *externalapi.DomainTransaction {
|
|
return func(tx *externalapi.DomainTransaction) *externalapi.DomainTransaction {
|
|
clone := tx.Clone()
|
|
clone.Inputs[inputIndex].PreviousOutpoint.Index = 2
|
|
return clone
|
|
}
|
|
}
|
|
|
|
func modifyAmountSpent(inputIndex int) func(tx *externalapi.DomainTransaction) *externalapi.DomainTransaction {
|
|
return func(tx *externalapi.DomainTransaction) *externalapi.DomainTransaction {
|
|
clone := tx.Clone()
|
|
utxoEntry := clone.Inputs[inputIndex].UTXOEntry
|
|
clone.Inputs[inputIndex].UTXOEntry = utxo.NewUTXOEntry(666, utxoEntry.ScriptPublicKey(), false, 100)
|
|
return clone
|
|
}
|
|
}
|
|
|
|
func modifyScriptPublicKey(inputIndex int) func(tx *externalapi.DomainTransaction) *externalapi.DomainTransaction {
|
|
return func(tx *externalapi.DomainTransaction) *externalapi.DomainTransaction {
|
|
clone := tx.Clone()
|
|
utxoEntry := clone.Inputs[inputIndex].UTXOEntry
|
|
scriptPublicKey := utxoEntry.ScriptPublicKey()
|
|
scriptPublicKey.Script = append(scriptPublicKey.Script, 1, 2, 3)
|
|
clone.Inputs[inputIndex].UTXOEntry = utxo.NewUTXOEntry(utxoEntry.Amount(), scriptPublicKey, false, 100)
|
|
return clone
|
|
}
|
|
}
|
|
|
|
func modifySequence(inputIndex int) func(tx *externalapi.DomainTransaction) *externalapi.DomainTransaction {
|
|
return func(tx *externalapi.DomainTransaction) *externalapi.DomainTransaction {
|
|
clone := tx.Clone()
|
|
clone.Inputs[inputIndex].Sequence = 12345
|
|
return clone
|
|
}
|
|
}
|
|
|
|
func modifyPayload(tx *externalapi.DomainTransaction) *externalapi.DomainTransaction {
|
|
clone := tx.Clone()
|
|
clone.Payload = []byte{6, 6, 6, 4, 2, 0, 1, 3, 3, 7}
|
|
return clone
|
|
}
|
|
|
|
func modifyGas(tx *externalapi.DomainTransaction) *externalapi.DomainTransaction {
|
|
clone := tx.Clone()
|
|
clone.Gas = 1234
|
|
return clone
|
|
}
|
|
|
|
func modifySubnetworkID(tx *externalapi.DomainTransaction) *externalapi.DomainTransaction {
|
|
clone := tx.Clone()
|
|
clone.SubnetworkID = externalapi.DomainSubnetworkID{6, 6, 6, 4, 2, 0, 1, 3, 3, 7}
|
|
return clone
|
|
}
|
|
|
|
func TestCalculateSignatureHash(t *testing.T) {
|
|
nativeTx, subnetworkTx, err := generateTxs()
|
|
if err != nil {
|
|
t.Fatalf("Error from generateTxs: %+v", err)
|
|
}
|
|
|
|
// Note: Expected values were generated by the same code that they test,
|
|
// As long as those were not verified using 3rd-party code they only check for regression, not correctness
|
|
tests := []struct {
|
|
name string
|
|
tx *externalapi.DomainTransaction
|
|
hashType consensushashing.SigHashType
|
|
inputIndex int
|
|
modificationFunction func(*externalapi.DomainTransaction) *externalapi.DomainTransaction
|
|
expectedSignatureHash string
|
|
}{
|
|
// native transactions
|
|
|
|
// sigHashAll
|
|
{name: "native-all-0", tx: nativeTx, hashType: all, inputIndex: 0,
|
|
expectedSignatureHash: "3e4a8effa6903dea5f762754ec410d732114ec2907e5bcbae7b6dd8d3f309a10"},
|
|
{name: "native-all-0-modify-input-1", tx: nativeTx, hashType: all, inputIndex: 0,
|
|
modificationFunction: modifyInput(1), // should change the hash
|
|
expectedSignatureHash: "0bd2947383101f9708d94d5799626c69c1b8472d2de66523c90c4a674e99cc51"},
|
|
{name: "native-all-0-modify-output-1", tx: nativeTx, hashType: all, inputIndex: 0,
|
|
modificationFunction: modifyOutput(1), // should change the hash
|
|
expectedSignatureHash: "ae69aa1372e958f069bf52d2628ead7ee789f195340b615ff0bcb6f01a995810"},
|
|
{name: "native-all-0-modify-sequence-1", tx: nativeTx, hashType: all, inputIndex: 0,
|
|
modificationFunction: modifySequence(1), // should change the hash
|
|
expectedSignatureHash: "51295575e7efc1fe1c2e741ade49089e3d780d15d26e9a0b18b3d90e35caf795"},
|
|
{name: "native-all-anyonecanpay-0", tx: nativeTx, hashType: allAnyoneCanPay, inputIndex: 0,
|
|
expectedSignatureHash: "0a13d3cab42a6cf3a7ef96f7b28c9bb0d98c209a3032ff85a6bfa7dac520f2c2"},
|
|
{name: "native-all-anyonecanpay-0-modify-input-0", tx: nativeTx, hashType: allAnyoneCanPay, inputIndex: 0,
|
|
modificationFunction: modifyInput(0), // should change the hash
|
|
expectedSignatureHash: "aeaa56f5bc99daea0be5ed4b047808ce0123a81ac89c6089b72fa7199f5cd1c6"},
|
|
{name: "native-all-anyonecanpay-0-modify-input-1", tx: nativeTx, hashType: allAnyoneCanPay, inputIndex: 0,
|
|
modificationFunction: modifyInput(1), // shouldn't change the hash
|
|
expectedSignatureHash: "0a13d3cab42a6cf3a7ef96f7b28c9bb0d98c209a3032ff85a6bfa7dac520f2c2"},
|
|
{name: "native-all-anyonecanpay-0-modify-sequence", tx: nativeTx, hashType: allAnyoneCanPay, inputIndex: 0,
|
|
modificationFunction: modifySequence(1), // shouldn't change the hash
|
|
expectedSignatureHash: "0a13d3cab42a6cf3a7ef96f7b28c9bb0d98c209a3032ff85a6bfa7dac520f2c2"},
|
|
|
|
// sigHashNone
|
|
{name: "native-none-0", tx: nativeTx, hashType: none, inputIndex: 0,
|
|
expectedSignatureHash: "da53f7c726b55357adb1b644265fe7b9b7897cadde91a942d6127195c2ce99dc"},
|
|
{name: "native-none-0-modify-output-1", tx: nativeTx, hashType: none, inputIndex: 0,
|
|
modificationFunction: modifyOutput(1), // shouldn't change the hash
|
|
expectedSignatureHash: "da53f7c726b55357adb1b644265fe7b9b7897cadde91a942d6127195c2ce99dc"},
|
|
{name: "native-none-0-modify-sequence-0", tx: nativeTx, hashType: none, inputIndex: 0,
|
|
modificationFunction: modifySequence(0), // should change the hash
|
|
expectedSignatureHash: "72c07c152a3792fb863d2de219ab4e863fe6779dc970a5c3958e26b3a3b9f139"},
|
|
{name: "native-none-0-modify-sequence-1", tx: nativeTx, hashType: none, inputIndex: 0,
|
|
modificationFunction: modifySequence(1), // shouldn't change the hash
|
|
expectedSignatureHash: "da53f7c726b55357adb1b644265fe7b9b7897cadde91a942d6127195c2ce99dc"},
|
|
{name: "native-none-anyonecanpay-0", tx: nativeTx, hashType: noneAnyoneCanPay, inputIndex: 0,
|
|
expectedSignatureHash: "18eb79df328a516708f792cadfc4bf2be21b6add35fb6637a20347d532b1dce1"},
|
|
{name: "native-none-anyonecanpay-0-modify-amount-spent", tx: nativeTx, hashType: noneAnyoneCanPay, inputIndex: 0,
|
|
modificationFunction: modifyAmountSpent(0), // should change the hash
|
|
expectedSignatureHash: "674a8e6effa0bbfdb3df3ca45a7b17ab695cc0f9b3e0519e5bff165de13604e2"},
|
|
{name: "native-none-anyonecanpay-0-modify-script-public-key", tx: nativeTx, hashType: noneAnyoneCanPay, inputIndex: 0,
|
|
modificationFunction: modifyScriptPublicKey(0), // should change the hash
|
|
expectedSignatureHash: "7a879d339c9b948c5264f1c0b8463f551221b2dcd575623f178cbbfcf7e01987"},
|
|
|
|
// sigHashSingle
|
|
{name: "native-single-0", tx: nativeTx, hashType: single, inputIndex: 0,
|
|
expectedSignatureHash: "99c0a4a381fed9dbd651450d6ca969a6e8cdd941e9d73be086a1ba6c90fb630f"},
|
|
{name: "native-single-0-modify-output-0", tx: nativeTx, hashType: single, inputIndex: 0,
|
|
modificationFunction: modifyOutput(0), // should change the hash
|
|
expectedSignatureHash: "92189a32391ca50a454d1853efed55acb1c49993911a1201df9891c866c483ee"},
|
|
{name: "native-single-0-modify-output-1", tx: nativeTx, hashType: single, inputIndex: 0,
|
|
modificationFunction: modifyOutput(1), // shouldn't change the hash
|
|
expectedSignatureHash: "99c0a4a381fed9dbd651450d6ca969a6e8cdd941e9d73be086a1ba6c90fb630f"},
|
|
{name: "native-single-0-modify-sequence-0", tx: nativeTx, hashType: single, inputIndex: 0,
|
|
modificationFunction: modifySequence(0), // should change the hash
|
|
expectedSignatureHash: "765e2289df98b3a5269f112d4b36d57fe32c74d42e04a3046c6a3c8dd78a4121"},
|
|
{name: "native-single-0-modify-sequence-1", tx: nativeTx, hashType: single, inputIndex: 0,
|
|
modificationFunction: modifySequence(1), // shouldn't change the hash
|
|
expectedSignatureHash: "99c0a4a381fed9dbd651450d6ca969a6e8cdd941e9d73be086a1ba6c90fb630f"},
|
|
{name: "native-single-2-no-corresponding-output", tx: nativeTx, hashType: single, inputIndex: 2,
|
|
expectedSignatureHash: "43de18c04d7fde81f49a40228d8730b4ceb0c66c77841c22622f59554769dd13"},
|
|
{name: "native-single-2-no-corresponding-output-modify-output-1", tx: nativeTx, hashType: single, inputIndex: 2,
|
|
modificationFunction: modifyOutput(1), // shouldn't change the hash
|
|
expectedSignatureHash: "43de18c04d7fde81f49a40228d8730b4ceb0c66c77841c22622f59554769dd13"},
|
|
{name: "native-single-anyonecanpay-0", tx: nativeTx, hashType: singleAnyoneCanPay, inputIndex: 0,
|
|
expectedSignatureHash: "2e270f86fd68f780a5aa8d250364ab6786d990040268e5d561d09dde365dfab7"},
|
|
{name: "native-single-anyonecanpay-2-no-corresponding-output", tx: nativeTx, hashType: singleAnyoneCanPay, inputIndex: 2,
|
|
expectedSignatureHash: "afc05dd6b4a530cc3a4d7d23126548bd1f31c793e9282cbbfa27ff5566219501"},
|
|
|
|
// subnetwork transaction
|
|
{name: "subnetwork-all-0", tx: subnetworkTx, hashType: all, inputIndex: 0,
|
|
expectedSignatureHash: "5a67423ee048e067b94e2d4fc2960f62eceff6aa8b6c5ad71e3b7b7e5ff6bad7"},
|
|
{name: "subnetwork-all-modify-payload", tx: subnetworkTx, hashType: all, inputIndex: 0,
|
|
modificationFunction: modifyPayload, // should change the hash
|
|
expectedSignatureHash: "0d3bc5914da8dc8df081945fea1255359f380ca9baa8b31dfb3657c1e3c6038a"},
|
|
{name: "subnetwork-all-modify-gas", tx: subnetworkTx, hashType: all, inputIndex: 0,
|
|
modificationFunction: modifyGas, // should change the hash
|
|
expectedSignatureHash: "70abe9f947d0a0f5d735f9a063db8af41fe5902940f2693a1782119063097094"},
|
|
{name: "subnetwork-all-subnetwork-id", tx: subnetworkTx, hashType: all, inputIndex: 0,
|
|
modificationFunction: modifySubnetworkID, // should change the hash
|
|
expectedSignatureHash: "571a0b7ea905b7a6ff7ab825b72d23f911bac0bfaa7c4c97a4887a3d090925d4"},
|
|
}
|
|
|
|
for _, test := range tests {
|
|
tx := test.tx
|
|
if test.modificationFunction != nil {
|
|
tx = test.modificationFunction(tx)
|
|
}
|
|
|
|
actualSignatureHash, err := consensushashing.CalculateSignatureHash(
|
|
tx, test.inputIndex, test.hashType, &consensushashing.SighashReusedValues{})
|
|
if err != nil {
|
|
t.Errorf("%s: Error from CalculateSignatureHash: %+v", test.name, err)
|
|
continue
|
|
}
|
|
|
|
if actualSignatureHash.String() != test.expectedSignatureHash {
|
|
t.Errorf("%s: expected signature hash: '%s'; but got: '%s'",
|
|
test.name, test.expectedSignatureHash, actualSignatureHash)
|
|
}
|
|
}
|
|
}
|
|
|
|
func generateTxs() (nativeTx, subnetworkTx *externalapi.DomainTransaction, err error) {
|
|
genesisCoinbase := dagconfig.SimnetParams.GenesisBlock.Transactions[0]
|
|
genesisCoinbaseTransactionID := consensushashing.TransactionID(genesisCoinbase)
|
|
|
|
address1Str := "kaspasim:qzpj2cfa9m40w9m2cmr8pvfuqpp32mzzwsuw6ukhfduqpp32mzzws59e8fapc"
|
|
address1, err := util.DecodeAddress(address1Str, util.Bech32PrefixKaspaSim)
|
|
if err != nil {
|
|
return nil, nil, fmt.Errorf("error decoding address1: %+v", err)
|
|
}
|
|
address1ToScript, err := txscript.PayToAddrScript(address1)
|
|
if err != nil {
|
|
return nil, nil, fmt.Errorf("error generating script: %+v", err)
|
|
}
|
|
|
|
address2Str := "kaspasim:qr7w7nqsdnc3zddm6u8s9fex4ysk95hm3v30q353ymuqpp32mzzws59e8fapc"
|
|
address2, err := util.DecodeAddress(address2Str, util.Bech32PrefixKaspaSim)
|
|
if err != nil {
|
|
return nil, nil, fmt.Errorf("error decoding address2: %+v", err)
|
|
}
|
|
address2ToScript, err := txscript.PayToAddrScript(address2)
|
|
if err != nil {
|
|
return nil, nil, fmt.Errorf("error generating script: %+v", err)
|
|
}
|
|
|
|
txIns := []*externalapi.DomainTransactionInput{
|
|
{
|
|
PreviousOutpoint: *externalapi.NewDomainOutpoint(genesisCoinbaseTransactionID, 0),
|
|
Sequence: 0,
|
|
UTXOEntry: utxo.NewUTXOEntry(100, address1ToScript, false, 0),
|
|
},
|
|
{
|
|
PreviousOutpoint: *externalapi.NewDomainOutpoint(genesisCoinbaseTransactionID, 1),
|
|
Sequence: 1,
|
|
UTXOEntry: utxo.NewUTXOEntry(200, address2ToScript, false, 0),
|
|
},
|
|
{
|
|
PreviousOutpoint: *externalapi.NewDomainOutpoint(genesisCoinbaseTransactionID, 2),
|
|
Sequence: 2,
|
|
UTXOEntry: utxo.NewUTXOEntry(300, address2ToScript, false, 0),
|
|
},
|
|
}
|
|
|
|
txOuts := []*externalapi.DomainTransactionOutput{
|
|
{
|
|
Value: 300,
|
|
ScriptPublicKey: address2ToScript,
|
|
},
|
|
{
|
|
Value: 300,
|
|
ScriptPublicKey: address1ToScript,
|
|
},
|
|
}
|
|
|
|
nativeTx = &externalapi.DomainTransaction{
|
|
Version: 0,
|
|
Inputs: txIns,
|
|
Outputs: txOuts,
|
|
LockTime: 1615462089000,
|
|
SubnetworkID: externalapi.DomainSubnetworkID{1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
|
|
}
|
|
subnetworkTx = &externalapi.DomainTransaction{
|
|
Version: 0,
|
|
Inputs: txIns,
|
|
Outputs: txOuts,
|
|
LockTime: 1615462089000,
|
|
SubnetworkID: externalapi.DomainSubnetworkID{1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
|
|
Gas: 250,
|
|
Payload: []byte{10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20},
|
|
}
|
|
|
|
return nativeTx, subnetworkTx, nil
|
|
}
|
|
|
|
func BenchmarkCalculateSignatureHash(b *testing.B) {
|
|
sigHashTypes := []consensushashing.SigHashType{
|
|
consensushashing.SigHashAll,
|
|
consensushashing.SigHashNone,
|
|
consensushashing.SigHashSingle,
|
|
consensushashing.SigHashAll | consensushashing.SigHashAnyOneCanPay,
|
|
consensushashing.SigHashNone | consensushashing.SigHashAnyOneCanPay,
|
|
consensushashing.SigHashSingle | consensushashing.SigHashAnyOneCanPay}
|
|
|
|
for _, size := range []int{10, 100, 1000} {
|
|
tx := generateTransaction(b, sigHashTypes, size)
|
|
|
|
b.Run(fmt.Sprintf("%d-inputs-and-outputs", size), func(b *testing.B) {
|
|
for i := 0; i < b.N; i++ {
|
|
reusedValues := &consensushashing.SighashReusedValues{}
|
|
for inputIndex := range tx.Inputs {
|
|
sigHashType := sigHashTypes[inputIndex%len(sigHashTypes)]
|
|
_, err := consensushashing.CalculateSignatureHash(tx, inputIndex, sigHashType, reusedValues)
|
|
if err != nil {
|
|
b.Fatalf("Error from CalculateSignatureHash: %+v", err)
|
|
}
|
|
}
|
|
}
|
|
})
|
|
}
|
|
}
|
|
|
|
func generateTransaction(b *testing.B, sigHashTypes []consensushashing.SigHashType, inputAndOutputSizes int) *externalapi.DomainTransaction {
|
|
sourceScript := getSourceScript(b)
|
|
tx := &externalapi.DomainTransaction{
|
|
Version: 0,
|
|
Inputs: generateInputs(inputAndOutputSizes, sourceScript),
|
|
Outputs: generateOutputs(inputAndOutputSizes, sourceScript),
|
|
LockTime: 123456789,
|
|
SubnetworkID: externalapi.DomainSubnetworkID{1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
|
|
Gas: 125,
|
|
Payload: []byte{9, 8, 7, 6, 5, 4, 3, 2, 1},
|
|
Fee: 0,
|
|
Mass: 0,
|
|
ID: nil,
|
|
}
|
|
signTx(b, tx, sigHashTypes)
|
|
return tx
|
|
}
|
|
|
|
func signTx(b *testing.B, tx *externalapi.DomainTransaction, sigHashTypes []consensushashing.SigHashType) {
|
|
sourceAddressPKStr := "a4d85b7532123e3dd34e58d7ce20895f7ca32349e29b01700bb5a3e72d2570eb"
|
|
privateKeyBytes, err := hex.DecodeString(sourceAddressPKStr)
|
|
if err != nil {
|
|
b.Fatalf("Error parsing private key hex: %+v", err)
|
|
}
|
|
keyPair, err := secp256k1.DeserializeSchnorrPrivateKeyFromSlice(privateKeyBytes)
|
|
if err != nil {
|
|
b.Fatalf("Error deserializing private key: %+v", err)
|
|
}
|
|
for i, txIn := range tx.Inputs {
|
|
signatureScript, err := txscript.SignatureScript(
|
|
tx, i, sigHashTypes[i%len(sigHashTypes)], keyPair, &consensushashing.SighashReusedValues{})
|
|
if err != nil {
|
|
b.Fatalf("Error from SignatureScript: %+v", err)
|
|
}
|
|
txIn.SignatureScript = signatureScript
|
|
}
|
|
|
|
}
|
|
|
|
func generateInputs(size int, sourceScript *externalapi.ScriptPublicKey) []*externalapi.DomainTransactionInput {
|
|
inputs := make([]*externalapi.DomainTransactionInput, size)
|
|
|
|
for i := 0; i < size; i++ {
|
|
inputs[i] = &externalapi.DomainTransactionInput{
|
|
PreviousOutpoint: *externalapi.NewDomainOutpoint(
|
|
externalapi.NewDomainTransactionIDFromByteArray(&[32]byte{12, 3, 4, 5}), 1),
|
|
SignatureScript: nil,
|
|
Sequence: uint64(i),
|
|
UTXOEntry: utxo.NewUTXOEntry(uint64(i), sourceScript, false, 12),
|
|
}
|
|
}
|
|
|
|
return inputs
|
|
}
|
|
|
|
func getSourceScript(b *testing.B) *externalapi.ScriptPublicKey {
|
|
sourceAddressStr := "kaspasim:qz6f9z6l3x4v3lf9mgf0t934th4nx5kgzu663x9yjh"
|
|
|
|
sourceAddress, err := util.DecodeAddress(sourceAddressStr, util.Bech32PrefixKaspaSim)
|
|
if err != nil {
|
|
b.Fatalf("Error from DecodeAddress: %+v", err)
|
|
}
|
|
|
|
sourceScript, err := txscript.PayToAddrScript(sourceAddress)
|
|
if err != nil {
|
|
b.Fatalf("Error from PayToAddrScript: %+v", err)
|
|
}
|
|
return sourceScript
|
|
}
|
|
|
|
func generateOutputs(size int, script *externalapi.ScriptPublicKey) []*externalapi.DomainTransactionOutput {
|
|
outputs := make([]*externalapi.DomainTransactionOutput, size)
|
|
|
|
for i := 0; i < size; i++ {
|
|
outputs[i] = &externalapi.DomainTransactionOutput{
|
|
Value: uint64(i),
|
|
ScriptPublicKey: script,
|
|
}
|
|
}
|
|
|
|
return outputs
|
|
}
|