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;
using ll = long long;
using P = pair<int, int>;
const ll MOD = 1000000007;

vector<vector<pair<int, int>>> constranints;
int N, M;
int memo[302][302][302];

int dfs(int r, int g, int b, int k){
    if(memo[r][g][b] != -1) return memo[r][g][b];
    for(auto p : constranints[k]){
        int l = p.first, x = p.second;
        if(x != (l <= r) + (l <= g) + (l <= b)){
            return 0;
        }
    }
    if(k == N){
        return 1;
    }

    int ret = 0;
    ret = (ret + dfs(k+1, g, b, k+1)) % MOD;
    ret = (ret + dfs(r, k+1, b, k+1)) % MOD;
    ret = (ret + dfs(r, g, k+1, k+1)) % MOD;

    memo[r][g][b] = ret;
    return ret;
}

int main(){
    cin >> N >> M;

    constranints.assign(N+1, {});
    for(int i=0;i<M;i++){
        int l, r, x;
        cin >> l >> r >> x;
        constranints[r].emplace_back(l, x);
    }

    memset(memo, -1, sizeof(memo));
    cout << dfs(0, 0, 0, 0) << endl;

    return 0;
}