Graph and Cycles

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 [e[1], e[2], ..., e[k]] that has the following properties:

• k is greater than 1.

• For any i from 1 to k, an edge e[i] has exactly one common vertex with edge e[i-1] and exactly one common vertex with edge e[i+1] and these vertices are distinct (consider e[0] = e[k], e[k+1] = e[1]).

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

Let’s define f(e[1], e[2]) as a function that takes edges e[1] and e[2] as parameters and returns the maximum between the weights of e[1] and e[2].

Let’s say that we have a cycle-array C = [e[1], e[2], ..., e[k]]. Let’s define the price of a cycle-array as the sum of f(e[i], e[i+1]) for all i from 1 to k (consider e[k+1] = e[1]).

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.

Input

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 ≤ 10^9), meaning that there is an edge between the nodes u and v that has weight w.

Output

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

Examples

Note

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 = {[e[1], e[2], e[3]]}: f(e[1], e[2]) + f(e[2], e[3]) + f(e[3], e[1]) = 1 + 1 + 1 = 3.

The optimal cycle-split in the second sample is S = {[e[3], e[8], e[9]], [e[2], e[4], e[7], e[10], e[5], e[1], e[6]]}. The price of [e[3], e[8], e[9]] is equal to 12, the price of [e[2], e[4], e[7], e[10], e[5], e[1], e[6]] is equal to 23, thus the price of the split is equal to 35.