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;

const int mod = 1000*1000*1000 + 7;
int N, M;
struct Query {
    int l, x;
};
vector<vector<Query> > quer;

vector<vector<vector<int> > > cc;
int dp(int r, int g, int b) {
    int &ret = cc[r][g][b];
    if(ret != -1) return ret;

    int n = max(max(r, g), b);
    for(int i = 0; i < quer[n].size(); i++) {
        int l = quer[n][i].l, x = quer[n][i].x;
        if(r >= l) x--;
        if(g >= l) x--;
        if(b >= l) x--;
        if(x != 0) return ret = 0;
    }
    if(n == N) return 1;
    ret = dp(n + 1, g, b);
    ret += dp(r, n + 1, b); ret %= mod;
    ret += dp(r, g, n + 1); ret %= mod;
    return ret;
}

int main() {
    scanf("%d %d", &N, &M);
    quer.resize(N + 1);
    for(int i = 0; i < M; i++) {
        int l, r, x; scanf("%d %d %d", &l, &r, &x);
        quer[r].push_back({l, x});
    }
    cc = vector<vector<vector<int> > >(N + 1, vector<vector<int> >(N + 1, vector<int>(N + 1, -1)));
    int ans = dp(1, 0, 0);
    ans += dp(0, 1, 0); ans %= mod;
    ans += dp(0, 0, 1); ans %= mod;
    printf("%d", ans);
}