#include<iostream>
#include<algorithm>
#include<cstdio>
using namespace std;
#define maxn 10100

struct N
{
    int n1, n2, cost;
}e[maxn];

int fa[maxn];

bool cmp(N a, N b)
{
    return a.cost<b.cost;
}

void init()
{
    for(int i=0; i<maxn; i++)
        fa[i]=i;
}

int find1(int x)
{
    if(x==fa[x])
        return x;
    fa[x]=find1(fa[x]);
    return fa[x];
}

int main()
{
    int n,m;
    while(scanf("%d%d",&n,&m)&&(n||m))
    {
        init();
        for(int i=0; i<m; i++)
            scanf("%d%d%d",&e[i].n1,&e[i].n2,&e[i].cost);
        sort(e,e+m,cmp);
        int num=0;
        for(int i=0; i<m; i++)
        {
            int a=find1(e[i].n1);
            int b=find1(e[i].n2);
            if(a==b)
                continue;
            fa[a]=fa[b];
            num++;
            if(num==(n+1)/2)
            {
                cout << e[i].cost << endl;
                break;
            }
        }
    }
}
### Prompt

Please create a solution in Cpp to the following problem:

Problem Statement

You are given a connected undirected graph which has even numbers of nodes. A connected graph is a graph in which all nodes are connected directly or indirectly by edges.

Your task is to find a spanning tree whose median value of edges' costs is minimum. A spanning tree of a graph means that a tree which contains all nodes of the graph.



Input

The input consists of multiple datasets.

The format of each dataset is as follows.


n m
s_1 t_1 c_1
...
s_m t_m c_m


The first line contains an even number n (2 \leq n \leq 1,000) and an integer m (n-1 \leq m \leq 10,000). n is the nubmer of nodes and m is the number of edges in the graph.

Then m lines follow, each of which contains s_i (1 \leq s_i \leq n), t_i (1 \leq s_i \leq n, t_i \neq s_i) and c_i (1 \leq c_i \leq 1,000). This means there is an edge between the nodes s_i and t_i and its cost is c_i. There is no more than one edge which connects s_i and t_i.

The input terminates when n=0 and m=0. Your program must not output anything for this case.

Output

Print the median value in a line for each dataset.

Example

Input

2 1
1 2 5
4 6
1 2 1
1 3 2
1 4 3
2 3 4
2 4 5
3 4 6
8 17
1 4 767
3 1 609
8 3 426
6 5 972
8 1 607
6 4 51
5 1 683
3 6 451
3 4 630
8 7 912
3 7 43
4 7 421
3 5 582
8 4 538
5 7 832
1 6 345
8 2 608
0 0


Output

5
2
421

### Response

```cpp
#include<iostream>
#include<algorithm>
#include<cstdio>
using namespace std;
#define maxn 10100

struct N
{
    int n1, n2, cost;
}e[maxn];

int fa[maxn];

bool cmp(N a, N b)
{
    return a.cost<b.cost;
}

void init()
{
    for(int i=0; i<maxn; i++)
        fa[i]=i;
}

int find1(int x)
{
    if(x==fa[x])
        return x;
    fa[x]=find1(fa[x]);
    return fa[x];
}

int main()
{
    int n,m;
    while(scanf("%d%d",&n,&m)&&(n||m))
    {
        init();
        for(int i=0; i<m; i++)
            scanf("%d%d%d",&e[i].n1,&e[i].n2,&e[i].cost);
        sort(e,e+m,cmp);
        int num=0;
        for(int i=0; i<m; i++)
        {
            int a=find1(e[i].n1);
            int b=find1(e[i].n2);
            if(a==b)
                continue;
            fa[a]=fa[b];
            num++;
            if(num==(n+1)/2)
            {
                cout << e[i].cost << endl;
                break;
            }
        }
    }
}
```