Problem: There are N squares arranged in a row. The squares are numbered 1, 2, ..., N, from left to right.

Snuke is painting each square in red, green or blue. According to his aesthetic sense, the following M conditions must all be satisfied. The i-th condition is:

* There are exactly x_i different colors among squares l_i, l_i + 1, ..., r_i.



In how many ways can the squares be painted to satisfy all the conditions? Find the count modulo 10^9+7.

Constraints

* 1 ≤ N ≤ 300
* 1 ≤ M ≤ 300
* 1 ≤ l_i ≤ r_i ≤ N
* 1 ≤ x_i ≤ 3

Input

Input is given from Standard Input in the following format:


N M
l_1 r_1 x_1
l_2 r_2 x_2
:
l_M r_M x_M


Output

Print the number of ways to paint the squares to satisfy all the conditions, modulo 10^9+7.

Examples

Input

3 1
1 3 3


Output

6


Input

4 2
1 3 1
2 4 2


Output

6


Input

1 3
1 1 1
1 1 2
1 1 3


Output

0


Input

8 10
2 6 2
5 5 1
3 5 2
4 7 3
4 4 1
2 3 1
7 7 1
1 5 2
1 7 3
3 4 2


Output

108

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

using namespace std;
typedef long long ll;

#define MAX 305
#define mod 1000000007
ll dp[MAX][MAX][MAX];
vector<pair<int, int> > Q[MAX];

int main(void) {
    int n, m;
    ll ans = 0;
    scanf("%d%d", &n, &m);
    for(int i=0; i<m; i++) {
        int l, r, x;
        scanf("%d%d%d", &l, &r, &x);
        Q[r].emplace_back(l, x);
    }
    dp[0][0][0] = 1;
    for(int i=0; i<=n; i++) for(int j=0; j<=n; j++) for(int k=0; k<=n; k++) {
        if(dp[i][j][k] == 0) continue;
        int mx = max(i, max(j, k));
        bool ok = true;
        for(auto q : Q[mx]) {
            int cnt = 0;
            if(q.first <= i) cnt++;
            if(q.first <= j) cnt++;
            if(q.first <= k) cnt++;
            if(cnt != q.second) {ok = false; break;}
        }
        if(!ok) continue;
        dp[i][j][k] %= mod;
        if(mx == n) ans += dp[i][j][k];
        dp[mx+1][j][k] += dp[i][j][k];
        dp[i][mx+1][k] += dp[i][j][k];
        dp[i][j][mx+1] += dp[i][j][k];
    }
    ans %= mod;
    printf("%lld\n", ans);
    return 0;
}