#include <bits/stdc++.h>
#define REP(i,s,e) for(int i=(s); i<(e);i++)
#define rep(i,n) REP(i,0,n)
#define rep1(i,n) REP(i,1,n)
#define repe(i,n) for(auto &&i:n)
#define all(v) (v).begin(),(v).end()
#define decimal fixed<<setprecision(20)
#define fastcin() cin.tie(0);ios::sync_with_stdio(false)
using namespace std;
using LL = long long;
using Graph = vector<vector<int>>;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
const int INF = 1e9;
const LL LLINF = 1e16;

struct UnionFind {
    vector<int> data;
    UnionFind(int size) : data(size, -1){ }

    bool merge(int x, int y) {
        x = root(x); y = root(y);
        if (x == y) return false;
        if (data[y] < data[x]) swap(x, y);
        data[x] += data[y];
        data[y] = x;
        return true;
    }

    int root(int x) {
        return data[x]<0 ? x : (data[x]=root(data[x]));
    }

    int size(int x) {
        return -data[root(x)];
    }
};


struct edge{
    int src, to, cost;
};
using Edges = vector<edge>;

int kruskal(Edges &E, int V)
{
    sort(all(E), [](const edge &a, const edge &b)
    {
        return (a.cost < b.cost);
    });
    UnionFind tree(V);
    vector<int> MST;
    for(auto &e: E) {
        if(tree.merge(e.src, e.to)) MST.push_back(e.cost);
    }
    sort(all(MST));
    return MST[MST.size()/2];
}

int main(){
    fastcin();

    int n, m;
    cin >> n >> m;
    while(n > 0){
        Edges E(m);
        rep(i, m){
            int s, t, c;
            cin >> s >> t >> c;
            s--; t--;
            E[i] = edge({s, t, c});
        }
        cout << kruskal(E, n) << endl;
        cin >> n >> m;
    }
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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 <bits/stdc++.h>
#define REP(i,s,e) for(int i=(s); i<(e);i++)
#define rep(i,n) REP(i,0,n)
#define rep1(i,n) REP(i,1,n)
#define repe(i,n) for(auto &&i:n)
#define all(v) (v).begin(),(v).end()
#define decimal fixed<<setprecision(20)
#define fastcin() cin.tie(0);ios::sync_with_stdio(false)
using namespace std;
using LL = long long;
using Graph = vector<vector<int>>;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
const int INF = 1e9;
const LL LLINF = 1e16;

struct UnionFind {
    vector<int> data;
    UnionFind(int size) : data(size, -1){ }

    bool merge(int x, int y) {
        x = root(x); y = root(y);
        if (x == y) return false;
        if (data[y] < data[x]) swap(x, y);
        data[x] += data[y];
        data[y] = x;
        return true;
    }

    int root(int x) {
        return data[x]<0 ? x : (data[x]=root(data[x]));
    }

    int size(int x) {
        return -data[root(x)];
    }
};


struct edge{
    int src, to, cost;
};
using Edges = vector<edge>;

int kruskal(Edges &E, int V)
{
    sort(all(E), [](const edge &a, const edge &b)
    {
        return (a.cost < b.cost);
    });
    UnionFind tree(V);
    vector<int> MST;
    for(auto &e: E) {
        if(tree.merge(e.src, e.to)) MST.push_back(e.cost);
    }
    sort(all(MST));
    return MST[MST.size()/2];
}

int main(){
    fastcin();

    int n, m;
    cin >> n >> m;
    while(n > 0){
        Edges E(m);
        rep(i, m){
            int s, t, c;
            cin >> s >> t >> c;
            s--; t--;
            E[i] = edge({s, t, c});
        }
        cout << kruskal(E, n) << endl;
        cin >> n >> m;
    }
}

```