For a given weighted undirected graph G(V, E), find the distance of the shortest route that meets the following criteria:

* It is a closed cycle where it ends at the same point it starts.
* The route must go through every edge at least once.

Constraints

* 2 ≤ |V| ≤ 15
* 0 ≤ |E| ≤ 1,000
* 0 ≤ di ≤ 1,000
* si ≠ ti
* The graph is connected

Input


|V| |E|
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1


, where |V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively.

si and ti represent source and target verticess of i-th edge (undirected) and di represents the distance between si and ti (the i-th edge).

Note that there can be multiple edges between a pair of vertices.

Output

Print the shortest distance in a line.

Examples

Input

4 4
0 1 1
0 2 2
1 3 3
2 3 4


Output

10


Input

4 5
0 1 1
0 2 2
1 3 3
2 3 4
1 2 5


Output

18


Input

2 3
0 1 1
0 1 2
0 1 3


Output

7
#define _CRT_SECURE_NO_WARNINGS
// #define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
template<class T> ostream &operator << (ostream &os, const vector<T> &);
template<size_t n, class...T> typename enable_if<(n>=sizeof...(T))>::type _ot(ostream &, const tuple<T...> &){}
template<size_t n, class...T> typename enable_if<(n< sizeof...(T))>::type _ot(ostream &os, const tuple<T...> &t){
    os << (n == 0 ? "" : " ") << get<n>(t); _ot<n+1>(os, t);
}
template<class...T> ostream &operator << (ostream &os, const tuple<T...> &t){
    _ot<0>(os, t); return os;
}
template<class T, class U> ostream & operator << (ostream &os, const pair<T,U> &p){
    return os << "(" << p.first << ", " << p.second << ") ";
}
template<class T> ostream &operator << (ostream &os, const vector<T> &v){
    for(size_t i = 0; i < v.size(); i++) os << v[i] << (i + 1 == v.size() ? "" : ", "); return os;
}
#ifdef DEBUG
#define dump(...) (cerr << #__VA_ARGS__ << " = " << make_tuple(__VA_ARGS__) \
                   << " (L : " << __LINE__ << ")" << endl)
#else
#define dump(...)
#endif
#define all(c) begin(c), end(c)
#define range(i,a,b) for(int i = a; i < (int)(b); i++)
#define rep(i,b) range(i,0,b)
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
using ll = long long;
// #define int ll
using vi = vector<int>;
using vvi = vector<vi>;
using pii = pair<int,int>;
void fastios(){ ios_base::sync_with_stdio(0); cin.tie(0); }
int const mod = 1000000007;
auto const inf = numeric_limits<int>::max()/8;


using Weight = int;
using Capacity = int;
struct Edge {
    int src, dst; Weight weight;
    Edge(int s, int d, int w) : src(s), dst(d), weight(w) {}
};
using Edges = vector<Edge>;
using Graph = vector<Edges>;
using Array = vector<Weight>;
using Matrix = vector<Array>;

int chinesePostman(const Graph &g) {
    Weight total = 0;
    int n = g.size();
    vector<int> odds;
    static Weight dist[17][17];
    for(int i = 0; i < n; ++i){
        fill(dist[i], dist[i]+n, inf);
        for(auto &e : g[i]){
            int s = e.src, d = e.dst; Weight w = e.weight;
            total += w;
            dist[s][d] = min(dist[s][d], w);
        }
        if(g[i].size() % 2 == 1) odds.push_back(i);
    }
    for(int k = 0; k < n; ++k){
        for(int i = 0; i < n; ++i){
            for(int j = 0; j < n; ++j){
                dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j]);
            }
        }
    }
    static Weight dp[1<<17];
    int k = odds.size();
    fill(dp, dp+(1<<k), inf);
    dp[0] = 0;
    for(int S = 0; S < 1<<k; ++S){
        for(int i = 0; i < k; ++i){
            if(S >> i & 1) continue;
            for(int j = 0; j < i; j++){
                if(S >> j & 1) continue;
                dp[S|1<<i|1<<j] = min(dp[S|1<<i|1<<j], dp[S] + dist[odds[i]][odds[j]]);
            }
        }
    }
    return total/2 + dp[(1<<k)-1];
}

int main(){
    int n,m;
    while(cin >> n >> m){
        Graph g(n);
        rep(i,m){
            int a,b,c;
            cin >> a >> b >> c;
            g[a].eb(a,b,c);
            g[b].eb(b,a,c);
        }
        cout << chinesePostman(g) << endl;
    }
}