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tree_distanceequaltriad_counting_diff_5_0_3255b2aa4b
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 6\n6 8\n5 6\n2 7\n2 9\n2 4\n3 5\n2 6\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_1_abb45ed5ff
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n2 4\n4 6\n1 5\n6 7\n6 8\n5 9\n5 7\n3 6\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_2_6a83ec3652
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n5 9\n1 2\n4 5\n6 8\n6 7\n2 8\n4 7\n3 8\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_3_cf5f13aa8d
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n2 6\n6 9\n1 7\n5 6\n3 4\n6 7\n5 8\n1 3\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_4_829c927af2
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 3\n7 9\n4 6\n3 8\n2 3\n2 7\n5 9\n2 6\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_5_2139047d48
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 3\n1 6\n1 8\n4 5\n2 3\n4 7\n3 4\n2 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_6_a598e0ca98
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n3 8\n6 9\n1 4\n5 6\n7 9\n3 5\n2 7\n4 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_7_cacc2857e0
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n3 5\n5 8\n2 4\n1 7\n2 9\n2 7\n4 6\n2 8\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_8_bfb72dde59
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 3\n1 6\n1 9\n3 5\n5 8\n5 7\n1 2\n4 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_9_8319dbe6d2
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 2\n1 5\n4 9\n4 7\n3 7\n6 8\n5 7\n2 6\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_10_f285c040ad
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 5\n3 7\n4 6\n2 6\n5 8\n6 8\n2 9\n3 6\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_11_28682dea20
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n3 8\n3 7\n2 7\n1 3\n5 7\n3 4\n1 6\n6 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_12_d852a5b24b
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n3 9\n3 5\n1 7\n1 6\n1 4\n7 8\n2 3\n1 2\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_13_f64a220dec
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n4 8\n7 9\n1 6\n2 5\n2 7\n3 4\n2 4\n1 4\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_14_bebdef3c72
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n5 6\n5 7\n1 9\n1 8\n2 5\n4 8\n1 5\n3 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_15_d7828ff7c4
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n7 9\n1 4\n3 9\n3 6\n1 7\n7 8\n2 7\n5 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_16_130c6a5245
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n5 8\n1 5\n1 7\n1 9\n3 6\n3 9\n4 5\n2 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_17_ed2da3ab43
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n5 6\n4 5\n1 8\n3 9\n2 4\n3 5\n1 4\n7 8\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_18_8c525750ac
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 9\n2 7\n5 7\n1 6\n3 9\n4 8\n7 8\n1 5\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_19_0bec9156c3
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n4 7\n2 7\n1 6\n6 7\n3 8\n6 9\n3 9\n5 7\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_20_7bb7498703
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n2 8\n2 7\n4 5\n8 9\n6 8\n4 8\n1 2\n3 5\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_21_053210ebbe
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n5 9\n2 3\n1 4\n2 5\n6 9\n1 5\n7 8\n5 8\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_22_5f40872146
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n8 9\n6 9\n2 6\n3 9\n5 6\n6 7\n1 9\n4 8\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_23_0b1973650b
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n4 6\n7 8\n1 6\n7 9\n3 4\n2 3\n2 5\n6 7\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_24_e4bd31ee7f
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 7\n2 5\n5 8\n2 3\n4 6\n1 8\n5 9\n1 4\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_25_9208e4ef3a
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n5 6\n7 8\n4 6\n6 8\n3 4\n5 9\n1 3\n2 3\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_26_d36023af05
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 7\n1 6\n1 4\n2 5\n1 9\n3 7\n5 8\n2 3\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_27_81c46f5a99
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n5 9\n7 8\n7 9\n4 7\n3 7\n1 7\n2 7\n6 7\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_28_834b4e3949
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n6 7\n6 8\n4 5\n3 5\n1 2\n4 8\n1 8\n4 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_29_36539bf7c1
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 8\n2 5\n4 5\n7 9\n4 7\n4 6\n4 8\n3 7\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_30_6f1aff1b89
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n3 5\n2 8\n2 4\n6 7\n1 3\n4 6\n2 9\n3 6\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_31_39c928081c
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n5 7\n1 8\n2 5\n3 9\n3 5\n4 5\n5 6\n3 8\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_32_20b6570edb
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 7\n2 4\n1 8\n1 6\n3 4\n5 6\n3 5\n7 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_33_74e465af45
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n4 6\n3 4\n5 6\n2 5\n1 8\n6 9\n2 7\n1 5\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_34_923710c560
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n7 9\n2 5\n2 7\n3 4\n1 4\n2 6\n3 8\n3 7\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_35_b260fc3fae
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n3 4\n1 4\n4 8\n5 9\n3 6\n2 4\n1 5\n2 7\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_36_574672c591
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n3 9\n2 4\n4 9\n5 9\n7 8\n5 7\n4 6\n1 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_37_2d7ae319af
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n6 9\n1 6\n2 5\n7 8\n3 8\n5 9\n4 8\n7 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_38_fa51ad2739
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n3 4\n2 4\n2 9\n1 3\n2 5\n1 7\n1 6\n2 8\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_39_688ca870f4
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 3\n4 6\n6 7\n7 8\n2 6\n1 5\n3 6\n7 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_40_8dc875f0be
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n6 7\n2 3\n1 6\n1 8\n4 5\n3 9\n4 9\n6 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_41_015d45c91e
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 5\n6 8\n1 4\n1 8\n3 9\n2 8\n7 9\n1 3\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_42_be744331b4
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n4 5\n7 8\n4 7\n2 4\n3 4\n1 7\n6 7\n4 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_43_4a35d43fb6
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n3 8\n3 6\n1 2\n2 4\n7 9\n8 9\n4 7\n4 5\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_44_fa810ade7c
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n6 9\n1 5\n5 6\n4 9\n3 5\n4 8\n7 8\n1 2\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_45_0d8a19b340
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n8 9\n1 8\n4 8\n2 3\n2 7\n6 8\n5 8\n2 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_46_8a4b5c8035
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n4 9\n7 8\n3 4\n4 5\n3 6\n4 8\n2 6\n1 4\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_47_807f7fddba
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 8\n1 4\n2 6\n1 7\n1 5\n3 9\n2 8\n1 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_48_c9ce42825a
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n3 9\n1 6\n2 5\n3 5\n1 7\n4 7\n7 8\n3 7\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_49_4fc9279853
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n7 8\n6 7\n2 3\n1 3\n5 9\n7 9\n3 9\n3 4\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_50_587a8d6040
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n2 7\n3 5\n1 6\n1 7\n1 8\n7 9\n4 9\n3 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_51_5cce3b4b2d
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n6 9\n1 3\n2 7\n5 6\n4 9\n8 9\n7 8\n1 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_52_4488a71c3c
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n2 7\n3 8\n1 9\n5 7\n3 6\n4 8\n2 9\n7 8\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_53_1254a51c08
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n2 6\n5 7\n6 8\n7 9\n1 7\n1 4\n1 2\n1 3\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_54_03b11c79fa
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n5 9\n1 2\n2 7\n1 6\n4 7\n1 9\n1 8\n3 6\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_55_be6f94e468
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 4\n5 7\n1 8\n7 8\n3 6\n1 3\n2 9\n1 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_56_aac2b6d7d3
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n4 6\n5 8\n2 3\n3 9\n7 8\n6 7\n1 7\n2 8\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_57_200373c485
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n5 7\n3 4\n2 4\n1 7\n7 8\n4 8\n2 9\n4 6\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_58_e869eaf0ad
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 5\n1 7\n1 9\n2 6\n2 4\n2 8\n3 5\n5 8\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_59_bc39175563
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n5 8\n2 6\n1 8\n3 5\n1 9\n5 7\n4 7\n6 7\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_60_0d53871749
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 6\n5 6\n1 9\n2 7\n1 4\n6 8\n3 7\n1 7\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_61_436b6b1632
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 6\n4 9\n1 7\n3 6\n2 7\n1 4\n6 8\n5 7\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_62_1ac6203098
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 9\n7 8\n1 5\n3 6\n5 8\n2 6\n1 4\n1 6\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_63_6726878a12
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n2 7\n5 6\n6 8\n4 9\n1 5\n2 6\n3 7\n4 6\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_64_0c068d0875
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n3 8\n1 3\n2 5\n1 5\n3 9\n6 9\n1 4\n3 7\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_65_c1e46bba4c
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n6 9\n1 2\n5 6\n1 4\n1 9\n3 4\n2 8\n4 7\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_66_95a76d6b94
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n6 8\n8 9\n1 3\n1 8\n1 7\n2 6\n4 9\n5 6\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_67_4116cff5d0
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 5\n3 4\n1 9\n1 6\n7 8\n1 3\n3 8\n2 8\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_68_5808095b73
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n4 6\n2 7\n3 6\n3 8\n6 9\n5 9\n3 7\n1 3\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_69_7da596faae
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 2\n8 9\n4 6\n6 7\n4 5\n2 9\n3 9\n3 6\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_70_f738f5b202
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n3 8\n1 2\n1 3\n4 9\n7 9\n8 9\n5 9\n1 6\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_71_c6f56002ee
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 3\n5 9\n2 9\n4 5\n5 8\n3 8\n1 6\n7 8\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_72_0cf363f873
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 7\n4 6\n4 9\n6 8\n1 5\n1 4\n3 8\n2 7\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_73_cb197c4bf5
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 9\n3 6\n4 8\n3 8\n3 7\n1 3\n5 7\n1 2\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_74_d71f99ee69
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n4 8\n6 7\n2 6\n4 6\n7 9\n1 8\n3 4\n4 5\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_75_c2e2f8afc3
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 3\n2 3\n1 7\n4 9\n2 6\n3 5\n6 9\n1 8\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_76_3b46279d44
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n3 6\n7 9\n8 9\n4 5\n5 7\n2 7\n1 7\n1 3\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_77_0e7164352b
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n5 6\n2 4\n3 4\n4 8\n7 9\n4 9\n2 6\n1 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_78_b7fbe6116b
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 8\n5 8\n6 9\n3 7\n2 8\n7 9\n4 9\n1 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_79_1961a2fd39
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n5 8\n4 7\n3 8\n4 6\n7 9\n2 7\n1 7\n4 5\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_80_21a930e2ef
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n2 3\n1 7\n5 9\n1 8\n4 9\n6 8\n1 2\n3 4\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_81_e5f1936f59
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n5 8\n2 5\n5 9\n1 7\n2 7\n2 3\n1 4\n6 7\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_82_839f753c88
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n2 9\n1 5\n1 6\n2 3\n4 8\n2 7\n1 4\n4 7\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_83_1e4fe61afa
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n3 7\n3 6\n3 9\n1 7\n4 6\n5 6\n2 8\n2 6\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_84_8d173e7e19
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 5\n2 9\n2 7\n2 6\n8 9\n3 6\n4 8\n1 6\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_85_0c0caf6490
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n5 9\n1 7\n4 7\n3 9\n6 8\n2 7\n6 9\n5 7\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_86_1b03c38d9f
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n6 8\n7 8\n5 9\n1 3\n4 5\n2 5\n2 3\n3 7\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_87_d8976b00b8
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n5 9\n1 2\n6 8\n6 9\n3 4\n6 7\n4 7\n2 8\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_88_26db536ba6
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 2\n4 5\n8 9\n5 8\n6 8\n1 9\n3 7\n3 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_89_f297d4c1ae
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 9\n1 4\n4 7\n5 9\n4 6\n6 8\n3 8\n2 4\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_90_11f73cc687
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n6 7\n4 7\n7 8\n3 8\n3 5\n1 2\n7 9\n1 8\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_91_1afe34c98b
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n4 8\n6 9\n7 8\n1 8\n8 9\n3 6\n5 8\n2 7\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_92_0a202e4170
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n3 6\n7 8\n2 4\n2 3\n2 8\n1 9\n1 2\n3 5\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_93_465c942467
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n2 9\n3 5\n3 7\n5 9\n7 8\n1 3\n4 5\n5 6\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_94_215caa01d0
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 5\n2 5\n6 8\n2 7\n5 9\n6 7\n2 4\n3 4\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_95_1c58e4594c
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n5 6\n5 7\n1 5\n2 7\n4 9\n3 8\n5 8\n4 8\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_96_f0b0920886
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n5 8\n5 9\n1 7\n2 5\n3 7\n4 6\n3 5\n3 4\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_97_c17c176906
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n1 2\n2 3\n2 9\n3 8\n4 7\n5 9\n5 7\n6 9\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_98_df6ba1024a
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n7 8\n2 7\n2 4\n5 7\n3 7\n5 9\n6 7\n1 3\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
tree_distanceequaltriad_counting_diff_5_99_86eec7709a
|
[
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices, labeled from `1` to `9`. It contains the following 8 undirected edges:\n3 4\n1 6\n2 5\n5 9\n5 8\n6 8\n1 3\n3 7\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 9) for which the **pairwise distances** are all equal — that is, the distance between A and B, between A and C, and between B and C are all the same. The distance between two vertices is the number of edges on the shortest path connecting them.",
"role": "user"
}
] |
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