시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 256 MB 6 6 6 100.000%

문제

There is an undirected weighted complete graph of n vertices where n is odd.

Let’s define a cycle-array of size k as an array of edges [e1, e2, . . . , ek] that has the following properties:

  • k is greater than 1.
  • For any i from 1 to k, an edge ei has exactly one common vertex with edge ei−1 and exactly one common vertex with edge ei+1 and these vertices are distinct (consider e0 = ek, ek+1 = e1).

It is obvious that edges in a cycle-array form a cycle.

Let’s define f(e1, e2) as a function that takes edges e1 and e2 as parameters and returns the maximum between the weights of e1 and e2.

Let’s say that we have a cycle-array C = [e1, e2, . . . , ek]. Let’s define the price of a cycle-array as the sum of f(ei, ei+1) for all i from 1 to k (consider ek+1 = e1).

Let’s define a cycle-split of a graph as a set of non-intersecting cycle-arrays, such that the union of them contains all of the edges of the graph. Let’s define the price of a cycle-split as the sum of prices of the arrays that belong to it.

There might be many possible cycle-splits of a graph. Given a graph, your task is to find the cycle-split with the minimum price and print the price of it.

입력

The first line contains one integer n (3 ≤ n ≤ 999, n is odd) — the number of nodes in the graph.

Each of the following n·(n−1)/2 lines contain three space-separated integers u, v and w (1 ≤ u, v ≤ n, u ≠ v, 1 ≤ w ≤ 109), meaning that there is an edge between the nodes u and v that has weight w.

출력

Print one integer — the minimum possible price of a cycle-split of the graph.

예제 입력 1

3
1 2 1
2 3 1
3 1 1

예제 출력 1

3

예제 입력 2

5
4 5 4
1 3 4
1 2 4
3 2 3
3 5 2
1 4 3
4 2 2
1 5 4
5 2 4
3 4 2

예제 출력 2

35

힌트

Let’s enumerate each edge in the same way as they appear in the input. I will use ei to represent the edge that appears i-th in the input.

The only possible cycle-split in the first sample is S = {[e1, e2, e3]}. f(e1, e2)+f(e2, e3)+f(e3, e1) = 1+1+1 = 3.

The optimal cycle-split in the second sample is S = {[e3, e8, e9], [e2, e4, e7, e10, e5, e1, e6]}. The price of [e3, e8, e9] is equal to 12, the price of [e2, e4, e7, e10, e5, e1, e6] is equal to 23, thus the price of the split is equal to 35.