{
  "insertion_tests": [
    {
      "leaf_preimages": [0, 1, 2, 3, 4, 5, 6, 7],
      "expected_roots": [
        "b151a956139bb821d4effa34ea95c17560e0135d1e4661fc23cedc3af49dac42"
      ]
    },
    {
      "leaf_preimages": [0, 1, 2, 3, 4, 5, 6],
      "expected_roots": [
        "df46b17be5f66f0750a4b3efa26d4679db170a72d41eb56c3e4ff75a58c65386",
        "9eec588c41d87b16b0ee226cb38da3864f9537632321d8be855a73d5616dcc73",
        "67586e98fad27da0b9968bc039a1ef34c939b9b8e523a8bef89d478608c5ecf6"
      ]
    },
    {
      "leaf_preimages": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14],
      "expected_roots": [
        "b151a956139bb821d4effa34ea95c17560e0135d1e4661fc23cedc3af49dac42",
        "9c053db406c1a077112189469a3aca0573d3481bef09fa3d2eda3304d7d44be8",
        "55d0a0ef8f5c25a9da266b36c0c5f4b31008ece82df2512c8966bddcc27a66a0",
        "4d7b3ef7300acf70c892d8327db8272f54434adbc61a4e130a563cb59a0d0f47"
      ]
    },
    {
      "leaf_preimages": [
        70, 13, 55, 152, 74, 33, 39, 122, 252, 53, 224, 211, 11, 25, 122, 14, 191, 152, 115,
        205, 160, 163, 90, 191, 199, 242, 216, 32, 141, 6, 200, 109, 211, 53, 72, 250, 108,
        163, 224, 90, 17, 25, 92, 254, 172, 211, 26, 231, 254, 159, 183, 180, 135, 131, 194,
        83, 207, 158, 226, 49, 138, 136, 73, 143, 105, 164, 50, 58, 94, 168, 90, 128, 132,
        238, 168, 47, 153, 20, 90, 106, 113, 168, 27, 136, 206, 3, 117, 87, 213, 48, 104, 7,
        59, 167, 164, 161, 151, 11, 63, 145, 61, 24, 40, 231, 49, 78, 86, 52, 208, 35, 97, 15,
        215, 238, 255, 227, 180, 226, 18, 223, 126, 157, 123, 81, 149, 46, 133, 132, 173, 190,
        87, 227, 139, 199, 209, 17, 210, 112, 204, 177, 71, 195, 56, 23, 67, 15, 226, 97, 62,
        7, 235, 63, 200, 140, 104, 4, 130, 47, 168, 33, 122, 118, 169, 129, 20, 186, 121, 114,
        107, 79, 215, 226, 45, 0, 108, 43, 53, 218, 252, 71, 176, 54, 93, 0, 168, 238, 209, 41,
        198, 111, 235, 215, 216, 60, 135, 230, 205, 177, 102
      ],
      "expected_roots": [
        "950c36521c4a3fa45862f31682f68b26af1e4a486fbf4d7f779a4bfcb8c9bbe9",
        "c9e5725dcf415c6eb0a2d381aa8b7678bc7a810ec46d8f330d4ef3ce023858bf",
        "a2402edac76acbf77c01dce0cdf0fbcf5e6e1acdf9eb97b891c2a6dc8582086a",
        "bb2202e245081accf9dfebba226acdef30ba221c8350ef5c707b0f9d294afe08",
        "252f10c83610ebca1a059c0bae8255eba2f95be4d1d7bcfa89d7248a82d9f111"
      ]
    }
  ],
  "proof_tests": [
    {
      "numleaves": 6,
      "roots": [
        "df46b17be5f66f0750a4b3efa26d4679db170a72d41eb56c3e4ff75a58c65386",
        "9eec588c41d87b16b0ee226cb38da3864f9537632321d8be855a73d5616dcc73"
      ],
      "targets": [],
      "target_preimages": [],
      "proofhashes": [],
      "expected": true
    },
    {
      "numleaves": 6,
      "roots": [
        "df46b17be5f66f0750a4b3efa26d4679db170a72d41eb56c3e4ff75a58c65386",
        "9eec588c41d87b16b0ee226cb38da3864f9537632321d8be855a73d5616dcc73"
      ],
      "targets": [0, 1, 2, 3],
      "target_preimages": [0, 1, 2, 3],
      "proofhashes": [],
      "expected": true
    },
    {
      "numleaves": 6,
      "roots": [
        "df46b17be5f66f0750a4b3efa26d4679db170a72d41eb56c3e4ff75a58c65386",
        "9eec588c41d87b16b0ee226cb38da3864f9537632321d8be855a73d5616dcc73"
      ],
      "targets": [4, 5],
      "target_preimages": [4, 5],
      "proofhashes": [],
      "expected": true
    },
    {
      "numleaves": 8,
      "roots": [
        "b151a956139bb821d4effa34ea95c17560e0135d1e4661fc23cedc3af49dac42"
      ],
      "targets": [0],
      "target_preimages": [0],
      "proofhashes": [
        "4bf5122f344554c53bde2ebb8cd2b7e3d1600ad631c385a5d7cce23c7785459a",
        "9576f4ade6e9bc3a6458b506ce3e4e890df29cb14cb5d3d887672aef55647a2b",
        "29590a14c1b09384b94a2c0e94bf821ca75b62eacebc47893397ca88e3bbcbd7"
      ],
      "expected": true
    },
    {
      "numleaves": 8,
      "roots": [
        "b151a956139bb821d4effa34ea95c17560e0135d1e4661fc23cedc3af49dac42"
      ],
      "targets": [5, 3, 1],
      "target_preimages": [5, 3, 1],
      "proofhashes": [
        "6e340b9cffb37a989ca544e6bb780a2c78901d3fb33738768511a30617afa01d",
        "dbc1b4c900ffe48d575b5da5c638040125f65db0fe3e24494b76ea986457d986",
        "e52d9c508c502347344d8c07ad91cbd6068afc75ff6292f062a09ca381c89e71",
        "34028bbc87000c39476cdc60cf80ca32d579b3a0e2d3f80e0ad8c3739a01aa91"
      ],
      "expected": true
    },
    {
      "numleaves": 8,
      "roots": [
        "859dad99dda0f8d0adb71f87a8b509fdfa9a0c1ab048399ca7b0da9fd6b258f8"
      ],
      "targets": [0, 9, 11],
      "target_preimages": [0, 3, 7],
      "proofhashes": [
        "4bf5122f344554c53bde2ebb8cd2b7e3d1600ad631c385a5d7cce23c7785459a",
        "9eec588c41d87b16b0ee226cb38da3864f9537632321d8be855a73d5616dcc73"
      ],
      "expected": true
    },
    {
      "numleaves": 8,
      "roots": [
        "b151a956139bb821d4effa34ea95c17560e0135d1e4661fc23cedc3af49dac42"
      ],
      "targets": [0],
      "target_preimages": [0],
      "proofhashes": [
        "7cf5122f344554c53bde2ebb8cd2b7e3d1600ad631c385a5d7cce23c7785459a",
        "9576f4ade6e9bc3a6458b506ce3e4e890df29cb14cb5d3d887672aef55647a2b",
        "29590a14c1b09384b94a2c0e94bf821ca75b62eacebc47893397ca88e3bbcbd7"
      ],
      "expected": false,
      "reason": "First proof hash is wrong"
    },
    {
      "numleaves": 8,
      "roots": [
        "b151a956139bb821d4effa34ea95c17560e0135d1e4661fc23cedc3af49dac42"
      ],
      "targets": [0, 1, 2],
      "target_preimages": [0, 1, 2],
      "proofhashes": [
        "084fed08b978af4d7d196a7446a86b58009e636b611db16211b65a9aadff29c5",
        "29590a14c1b09384b94a2c0e94bf821ca75b62eacebc47893397ca88e3bbcbd7"
      ],
      "expected": true
    },
    {
      "numleaves": 8,
      "roots": [
        "b151a956139bb821d4effa34ea95c17560e0135d1e4661fc23cedc3af49dac42"
      ],
      "targets": [1, 2, 6],
      "target_preimages": [1, 2, 6],
      "proofhashes": [
        "6e340b9cffb37a989ca544e6bb780a2c78901d3fb33738768511a30617afa01d",
        "084fed08b978af4d7d196a7446a86b58009e636b611db16211b65a9aadff29c5",
        "ca358758f6d27e6cf45272937977a748fd88391db679ceda7dc7bf1f005ee879",
        "9eec588c41d87b16b0ee226cb38da3864f9537632321d8be855a73d5616dcc73"
      ],
      "expected": true
    },
    {
      "numleaves": 20,
      "roots": [
        "e121f8ffd6ca510cb55fe2d6373de3d018f7d2e9fbecb3a6d8342e1f9f6e6c7a",
        "3cb920c113e8ce3ace35fc835e6ff83a6566c4c127ea67eebc0f5d25d2295ea2"
      ],
      "targets": [0, 5],
      "target_preimages": [0, 5],
      "proofhashes": [
        "4bf5122f344554c53bde2ebb8cd2b7e3d1600ad631c385a5d7cce23c7785459a",
        "e52d9c508c502347344d8c07ad91cbd6068afc75ff6292f062a09ca381c89e71",
        "9576f4ade6e9bc3a6458b506ce3e4e890df29cb14cb5d3d887672aef55647a2b",
        "34028bbc87000c39476cdc60cf80ca32d579b3a0e2d3f80e0ad8c3739a01aa91",
        "29a408b4bec8f8d5f3a45a0d733d096524269029a690d7d98b5ce627fef5ef36"
      ],
      "expected": true
    },
    {
      "numleaves": 100,
      "roots": [
        "72c32219411b8566bda58d4310b605f85a08b8eeb661b8c57e7ef09966fcc1eb",
        "0a2c57a002817e70a57e44d88ce570c3b197bd54047d5883b469c0ba0df6257e",
        "33436f0f467c317f77eb7bf06dd182e90fd41ad27d34d09923866d89f41c4c27"
      ],
      "targets": [20, 30, 31, 32],
      "target_preimages": [20, 30, 31, 32],
      "proofhashes": [
        "2f0fd1e89b8de1d57292742ec380ea47066e307ad645f5bc3adad8a06ff58608",
        "bb7208bc9b5d7c04f1236a82a0093a5e33f40423d5ba8d4266f7092c3ba43b62",
        "60e6d84b9ad3355211af775aff3338289431744c79fc06f5e2c065cbdd690f79",
        "9a899064135333436906fe5b714ca017e61d9e952860dcda410dec4bd0fd59a5",
        "18b41f49a19d41613b4f717b3ef291e2cde3b963fcf60f9a371affd761f1b998",
        "3cb920c113e8ce3ace35fc835e6ff83a6566c4c127ea67eebc0f5d25d2295ea2",
        "6faf95884aaf779221fbe2f81d68bbac26a70751d384fa5831b2d6d0cf07293d",
        "a8fdcb2277476c5a76bf6a5e1d107f5c48ec59a7c813f6f9f1419a648e5568af",
        "94b8dc9cecafe156b80e4e64414cf4204858f56713776c525c38fb14c2c5e622",
        "e121f8ffd6ca510cb55fe2d6373de3d018f7d2e9fbecb3a6d8342e1f9f6e6c7a",
        "8ec4ba1ba4d169b8a1e5261408d9799185d984206b1d8779e4a5c1e431023fc1"
      ],
      "expected": true
    },
    {
      "numleaves": 100,
      "roots": [
        "72c32219411b8566bda58d4310b605f85a08b8eeb661b8c57e7ef09966fcc1eb",
        "0a2c57a002817e70a57e44d88ce570c3b197bd54047d5883b469c0ba0df6257e",
        "33436f0f467c317f77eb7bf06dd182e90fd41ad27d34d09923866d89f41c4c27"
      ],
      "targets": [99, 20, 19, 10, 30, 32, 31],
      "target_preimages": [99, 20, 19, 10, 30, 32, 31],
      "proofhashes": [
        "e7cf46a078fed4fafd0b5e3aff144802b853f8ae459a4f0c14add3314b7cc3a6",
        "f299791cddd3d6664f6670842812ef6053eb6501bd6282a476bbbf3ee91e750c",
        "2f0fd1e89b8de1d57292742ec380ea47066e307ad645f5bc3adad8a06ff58608",
        "bb7208bc9b5d7c04f1236a82a0093a5e33f40423d5ba8d4266f7092c3ba43b62",
        "3e23e8160039594a33894f6564e1b1348bbd7a0088d42c4acb73eeaed59c009d",
        "cd9c77062a338e63a63ca623db438cb8676f15466641079ee61ec2dda98de796",
        "83b2d85c9ae3143b1b1598076c85b3830d7f35a6c67c6ad122df8ab6235c40a1",
        "60e6d84b9ad3355211af775aff3338289431744c79fc06f5e2c065cbdd690f79",
        "9a899064135333436906fe5b714ca017e61d9e952860dcda410dec4bd0fd59a5",
        "18b41f49a19d41613b4f717b3ef291e2cde3b963fcf60f9a371affd761f1b998",
        "46c5f8e5b7ccdb3eb2014f988c30a73ba8bacfccf282293acbe559e56d540a17",
        "e799acb98a071c4884707e4bc8c093ba22571c8d84cc0223ab0c2c9327313a5b",
        "6faf95884aaf779221fbe2f81d68bbac26a70751d384fa5831b2d6d0cf07293d",
        "a8fdcb2277476c5a76bf6a5e1d107f5c48ec59a7c813f6f9f1419a648e5568af",
        "b151a956139bb821d4effa34ea95c17560e0135d1e4661fc23cedc3af49dac42",
        "94b8dc9cecafe156b80e4e64414cf4204858f56713776c525c38fb14c2c5e622",
        "8ec4ba1ba4d169b8a1e5261408d9799185d984206b1d8779e4a5c1e431023fc1"
      ],
      "expected": true
    },
    {
      "numleaves": 100,
      "roots": [
        "72c32219411b8566bda58d4310b605f85a08b8eeb661b8c57e7ef09966fcc1eb",
        "0a2c57a002817e70a57e44d88ce570c3b197bd54047d5883b469c0ba0df6257e",
        "33436f0f467c317f77eb7bf06dd182e90fd41ad27d34d09923866d89f41c4c27"
      ],
      "targets": [20, 19, 10, 30, 31, 32, 99],
      "target_preimages": [20, 19, 10, 30, 31, 32, 99],
      "proofhashes": [
        "e7cf46a078fed4fafd0b5e3aff144802b853f8ae459a4f0c14add3314b7cc3a6",
        "f299791cddd3d6664f6670842812ef6053eb6501bd6282a476bbbf3ee91e750c",
        "2f0fd1e89b8de1d57292742ec380ea47066e307ad645f5bc3adad8a06ff58608",
        "bb7208bc9b5d7c04f1236a82a0093a5e33f40423d5ba8d4266f7092c3ba43b62",
        "3e23e8160039594a33894f6564e1b1348bbd7a0088d42c4acb73eeaed59c009d",
        "cd9c77062a338e63a63ca623db438cb8676f15466641079ee61ec2dda98de796",
        "83b2d85c9ae3143b1b1598076c85b3830d7f35a6c67c6ad122df8ab6235c40a1",
        "60e6d84b9ad3355211af775aff3338289431744c79fc06f5e2c065cbdd690f79",
        "9a899064135333436906fe5b714ca017e61d9e952860dcda410dec4bd0fd59a5",
        "18b41f49a19d41613b4f717b3ef291e2cde3b963fcf60f9a371affd761f1b998",
        "46c5f8e5b7ccdb3eb2014f988c30a73ba8bacfccf282293acbe559e56d540a17",
        "e799acb98a071c4884707e4bc8c093ba22571c8d84cc0223ab0c2c9327313a5b",
        "6faf95884aaf779221fbe2f81d68bbac26a70751d384fa5831b2d6d0cf07293d",
        "a8fdcb2277476c5a76bf6a5e1d107f5c48ec59a7c813f6f9f1419a648e5568af",
        "b151a956139bb821d4effa34ea95c17560e0135d1e4661fc23cedc3af49dac42",
        "94b8dc9cecafe156b80e4e64414cf4204858f56713776c525c38fb14c2c5e622",
        "8ec4ba1ba4d169b8a1e5261408d9799185d984206b1d8779e4a5c1e431023fc1"
      ],
      "expected": true
    }
  ],
  "deletion_tests": [
    {
      "leaf_preimages": [0, 1, 2, 3, 4, 5, 6, 7],
      "target_values": [1, 7],
      "proofhashes": [
        "6e340b9cffb37a989ca544e6bb780a2c78901d3fb33738768511a30617afa01d",
        "67586e98fad27da0b9968bc039a1ef34c939b9b8e523a8bef89d478608c5ecf6",
        "9576f4ade6e9bc3a6458b506ce3e4e890df29cb14cb5d3d887672aef55647a2b",
        "9eec588c41d87b16b0ee226cb38da3864f9537632321d8be855a73d5616dcc73"
      ],
      "expected_roots": [
        "332c306188d35eb22ecb05d8c00446cd6a7a475f6615f46207cfaa713bb3e62c"
      ]
    },
    {
      "leaf_preimages": [0, 1, 2, 3, 4, 5, 6, 7],
      "target_values": [1, 5, 7],
      "proofhashes": [
       "6e340b9cffb37a989ca544e6bb780a2c78901d3fb33738768511a30617afa01d",
       "e52d9c508c502347344d8c07ad91cbd6068afc75ff6292f062a09ca381c89e71",
       "67586e98fad27da0b9968bc039a1ef34c939b9b8e523a8bef89d478608c5ecf6",
       "9576f4ade6e9bc3a6458b506ce3e4e890df29cb14cb5d3d887672aef55647a2b"
      ],
      "expected_roots": [
        "3b8b6eb231437092f6d9fbf8a0696b7cb446e40f1bf81ddb23d3eabb3080b0dd"
      ]
    },
    {
      "leaf_preimages": [
        0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
      ],
      "target_values": [1, 10],
      "proofhashes": [
        "6e340b9cffb37a989ca544e6bb780a2c78901d3fb33738768511a30617afa01d",
        "e7cf46a078fed4fafd0b5e3aff144802b853f8ae459a4f0c14add3314b7cc3a6",
        "9576f4ade6e9bc3a6458b506ce3e4e890df29cb14cb5d3d887672aef55647a2b",
        "cd9c77062a338e63a63ca623db438cb8676f15466641079ee61ec2dda98de796",
        "29590a14c1b09384b94a2c0e94bf821ca75b62eacebc47893397ca88e3bbcbd7",
        "e799acb98a071c4884707e4bc8c093ba22571c8d84cc0223ab0c2c9327313a5b"
      ],
      "expected_roots": [
        "37968ef73d30dda38ede8357d66593c72acd4f0eb9f7a1a9acfeb7de850c05b4",
        "3cb920c113e8ce3ace35fc835e6ff83a6566c4c127ea67eebc0f5d25d2295ea2"
      ]
    },
    {
      "leaf_preimages": [
        0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
      ],
      "target_values": [1, 10, 16],
      "proofhashes": [
        "6e340b9cffb37a989ca544e6bb780a2c78901d3fb33738768511a30617afa01d",
        "e7cf46a078fed4fafd0b5e3aff144802b853f8ae459a4f0c14add3314b7cc3a6",
        "4a64a107f0cb32536e5bce6c98c393db21cca7f4ea187ba8c4dca8b51d4ea80a",
        "9576f4ade6e9bc3a6458b506ce3e4e890df29cb14cb5d3d887672aef55647a2b",
        "cd9c77062a338e63a63ca623db438cb8676f15466641079ee61ec2dda98de796",
        "96d56447466674521007145ed72f8757517c72f7737dc4a0dcd3ecb996968971",
        "29590a14c1b09384b94a2c0e94bf821ca75b62eacebc47893397ca88e3bbcbd7",
        "e799acb98a071c4884707e4bc8c093ba22571c8d84cc0223ab0c2c9327313a5b"
      ],
      "expected_roots": [
        "37968ef73d30dda38ede8357d66593c72acd4f0eb9f7a1a9acfeb7de850c05b4",
        "21326d8aebeb6ef7bc02f40bdf778a02ba1c836b257f946ae21cab2a6f95fa18"
      ]
    },
    {
      "leaf_preimages": [
        0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
      ],
      "target_values": [1, 10, 5],
      "proofhashes": [
        "6e340b9cffb37a989ca544e6bb780a2c78901d3fb33738768511a30617afa01d",
        "e52d9c508c502347344d8c07ad91cbd6068afc75ff6292f062a09ca381c89e71",
        "e7cf46a078fed4fafd0b5e3aff144802b853f8ae459a4f0c14add3314b7cc3a6",
        "9576f4ade6e9bc3a6458b506ce3e4e890df29cb14cb5d3d887672aef55647a2b",
        "34028bbc87000c39476cdc60cf80ca32d579b3a0e2d3f80e0ad8c3739a01aa91",
        "cd9c77062a338e63a63ca623db438cb8676f15466641079ee61ec2dda98de796"
      ],
      "expected_roots": [
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