For a given weighted directed 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.
* It visits each vertex exactly once.

Constraints

* 2 ≤ |V| ≤ 15
* 0 ≤ di ≤ 1,000
* There are no multiedge

Input


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


|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 vertices of i-th edge (directed) and di represents the distance between si and ti (the i-th edge).

Output

Print the shortest distance in a line. If there is no solution, print -1.

Examples

Input

4 6
0 1 2
1 2 3
1 3 9
2 0 1
2 3 6
3 2 4


Output

16


Input

3 3
0 1 1
1 2 1
0 2 1


Output

-1
#pragma GCC optimize ("O3")
#pragma GCC target ("avx")
#include "bits/stdc++.h" // define macro "/D__MAI"

using namespace std;
typedef long long int ll;

#define xprintf(fmt,...) fprintf(stderr,fmt,__VA_ARGS__)
#define debugv(v) {printf("L%d %s > ",__LINE__,#v);for(auto e:v){cout<<e<<" ";}cout<<endl;}
#define debuga(m,w) {printf("L%d %s > ",__LINE__,#m);for(int x=0;x<(w);x++){cout<<(m)[x]<<" ";}cout<<endl;}
#define debugaa(m,h,w) {printf("L%d %s >\n",__LINE__,#m);for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){cout<<(m)[y][x]<<" ";}cout<<endl;}}
#define ALL(v) (v).begin(),(v).end()
#define repeat(cnt,l) for(auto cnt=0ll;(cnt)<(l);++(cnt))
#define iterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);++(cnt))
#define MD 1000000007ll
#define PI 3.1415926535897932384626433832795
#define EPS 1e-12
template<typename T1, typename T2> ostream& operator <<(ostream &o, const pair<T1, T2> p) { o << "(" << p.first << ":" << p.second << ")"; return o; }
template<typename iterator> inline size_t argmin(iterator begin, iterator end) { return distance(begin, min_element(begin, end)); }
template<typename iterator> inline size_t argmax(iterator begin, iterator end) { return distance(begin, max_element(begin, end)); }
template<typename T> T& maxset(T& to, const T& val) { return to = max(to, val); }
template<typename T> T& minset(T& to, const T& val) { return to = min(to, val); }
void bye(string s, int code = 0) { cout << s << endl; exit(0); }
mt19937_64 randdev(8901016);
inline ll rand_range(ll l, ll h) {
    return uniform_int_distribution<ll>(l, h)(randdev);
}

#if defined(_WIN32) || defined(_WIN64)
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
#elif __GNUC__
#else
#define getchar_unlocked getchar
#define putchar_unlocked putchar
#endif
namespace {
#define isvisiblechar(c) (0x21<=(c)&&(c)<=0x7E)
    class MaiScanner {
    public:
        template<typename T> void input_integer(T& var) {
            var = 0; T sign = 1;
            int cc = getchar_unlocked();
            for (; cc<'0' || '9'<cc; cc = getchar_unlocked())
                if (cc == '-') sign = -1;
            for (; '0' <= cc&&cc <= '9'; cc = getchar_unlocked())
                var = (var << 3) + (var << 1) + cc - '0';
            var = var*sign;
        }
        inline int c() { return getchar_unlocked(); }
        inline MaiScanner& operator>>(int& var) { input_integer<int>(var); return *this; }
        inline MaiScanner& operator>>(long long& var) { input_integer<long long>(var); return *this; }
        inline MaiScanner& operator>>(string& var) {
            int cc = getchar_unlocked();
            for (; !isvisiblechar(cc); cc = getchar_unlocked());
            for (; isvisiblechar(cc); cc = getchar_unlocked())
                var.push_back(cc);
        }
        template<typename IT> void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; }
    };
    class MaiPrinter {
    public:
        template<typename T>
        void output_integer(T var) {
            if (var == 0) { putchar_unlocked('0'); return; }
            if (var < 0)
                putchar_unlocked('-'),
                var = -var;
            char stack[32]; int stack_p = 0;
            while (var)
                stack[stack_p++] = '0' + (var % 10),
                var /= 10;
            while (stack_p)
                putchar_unlocked(stack[--stack_p]);
        }
        inline MaiPrinter& operator<<(char c) { putchar_unlocked(c); return *this; }
        inline MaiPrinter& operator<<(int var) { output_integer<int>(var); return *this; }
        inline MaiPrinter& operator<<(long long var) { output_integer<long long>(var); return *this; }
        inline MaiPrinter& operator<<(char* str_p) { while (*str_p) putchar_unlocked(*(str_p++)); return *this; }
        inline MaiPrinter& operator<<(const string& str) {
            const char* p = str.c_str();
            const char* l = p + str.size();
            while (p < l) putchar_unlocked(*p++);
            return *this;
        }
        template<typename IT> void join(IT begin, IT end, char sep = '\n') { for (auto it = begin; it != end; ++it) *this << *it << sep; }
    };
}
MaiScanner scanner;
MaiPrinter printer;



class DGraph {
public:
    size_t n;
    vector<vector<int>> vertex_to;
    vector<vector<int>> vertex_from;

    DGraph(size_t n = 1) :n(n), vertex_to(n), vertex_from(n) {}

    void connect(int from, int to) {
        vertex_to[(size_t)from].emplace_back(to);
        vertex_from[(size_t)to].emplace_back(from);
    }
    void resize(size_t _n) {
        n = _n;
        vertex_to.resize(_n);
        vertex_from.resize(_n);
    }
};


class GraphE {
public:
    typedef int W_T;
    struct Edge {
        int u, v;
        W_T value;
        Edge(int from = 0, int to = 0, W_T value = 0) :u(from), v(to), value(value) {}
        inline int to(int _v) const { return _v == v ? u : v; }
    };
    size_t n;
    vector<vector<int>> vertex_to;
    vector<Edge> edges;

    GraphE(int n = 1) :n(n), vertex_to(n) { }

    void resize(size_t _n) {
        n = _n;
        vertex_to.resize(_n);
    }
    void connect(int from, int to, W_T val = 0) {
        vertex_to[(size_t)from].push_back((int)edges.size());
        vertex_to[(size_t)to].push_back((int)edges.size());
        edges.emplace_back(from, to, val);
    }
};

class Graph2d {
public:
    typedef ll W_T;
    size_t n;
    vector<W_T> matrix;

    Graph2d(size_t size) :n(size), matrix(size*size) {};

    void resize(size_t s) {
        n = s;
        matrix.resize(n*n);
    }

    inline W_T& at(int y, int x) { return matrix[y*n + x]; }
    inline W_T& operator()(int y, int x) { return matrix[y*n + x]; }
    inline W_T at(int y, int x) const { return matrix[y*n + x]; }
    inline W_T operator()(int y, int x) const { return matrix[y*n + x]; }

    inline void connect(int u, int v, W_T dist = 1) {
        at(u, v) = at(v, u) = dist;
    }
    inline void connect_d(int from, int to, W_T dist = 1) { // directedEdge u->v
        at(from, to) = dist;
    }
};




vector<int> tsProblem(int n, const Graph2d& graph) {
    typedef ll dist_T;
    typedef unsigned long long ull;

    if (n <= 1)
        return { 0 };
    if (n == 2)
        return { 0, 1 };

    vector<vector<dist_T>> dp;
    ull bit;

    // initialize
    dp.resize(n);
    for (auto &v : dp)
        v.resize(1 << n),
        fill(ALL(v), (dist_T)5e15);

    // bitdp
    dp[0][1] = 0;
    iterate(bit_i, 1, (1 << n) - 1) {
        bit = bit_i;

        repeat(from, n) {
            if (!(bool)(bit&(1ull << from))) continue;
            dist_T pt = dp[from][bit_i];

            repeat(to, n) {
                if ((bool)(bit&(1ull << to))) continue;
                dp[to][bit_i | (1ull << to)] = min(dp[to][bit_i | (1 << to)], pt + graph(from, to));
            }
        }
    }
    // ????°??????¢???
    dist_T best = 5e15;
    int tail = 0;
    repeat(i, n)
        if (dp[i][(1 << n) - 1] + graph(i, 0) < best)
            best = dp[i][(1 << n) - 1] + graph(i, 0), tail = i;

    // ??????
    vector<int> tourist; tourist.reserve(n);
    bit = (1ull << n) - 1ull;
    repeat(z, n - 1) {
        ull b = bit;
        tourist.push_back(tail);
        bit ^= bit & (1ull << tail);
        ull c = bit;

        repeat(nxt, n) {
            if ((bit&(1ull << (ull)nxt)) && abs(dp[tail][b] - dp[nxt][c] - graph(nxt, tail)) == 0) {
                tail = nxt;
                break;
            }
        }
    }
    tourist.push_back(0);
    reverse(ALL(tourist));
    return tourist;
}

int main() {

    int n, m;
    scanner >> n >> m;

    Graph2d dist(n);

    repeat(i, n)
        repeat(j, n)
            dist(i, j) = ll(1e7);


    repeat(i, m) {
        int s, t, d;
        scanner >> s >> t >> d;
        minset(dist(s, t), ll(d));
    }

    auto ans = tsProblem(n, dist);

    ll len = 0;
    {
        int p = ans.back();
        for (int t : ans)
            len += dist(p,t)
            p = t;
    }

    if (len >= ll(1e7))
        cout << -1 << endl;
    else
        cout << len << endl;

    return 0;
}