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;

#define LL long long
const int mod = 1e9 + 7;
int n, m, l, r, x, dp[305][305][305];
vector<pair<int,int>> v[305];

int solve(int a, int b, int c) {
    if(dp[a][b][c] != -1) return dp[a][b][c];
    int mx = max(a, max(b, c));

    for(auto x : v[mx]) if((a >= x.first) + (b >= x.first) + (c >= x.first) != x.second) return dp[a][b][c] = 0;
    if(mx == n) return dp[a][b][c] = 1;
    return dp[a][b][c] = ((solve(mx + 1, b, c) + solve(a, mx + 1, c)) % mod + solve(a, b, mx + 1)) % mod;     
}

int main() {
    ios::sync_with_stdio(0), cin.tie(0);
    
    cin >> n >> m;
    while(m--) {
        cin >> l >> r >> x;
        v[r].push_back({l, x});
    }        
    memset(dp, -1, sizeof dp);
    cout << solve(0, 0, 0);
}