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 <iostream>
#include <bits/stdc++.h>

#define si(x) scanf("%d",&x)

using namespace std;
const int MAXN = 301;
const int MOD = 1e9+7;
int dp[MAXN][MAXN][MAXN];
int n,q;
vector<pair<int,int> > endd[MAXN];

int solve(int r,int g,int b, int ind){
    int indd = max(max(r,g),b);
    if(endd[indd].size()!=0){
        for(int i=0;i<endd[indd].size();i++){
            int startt = endd[indd][i].first;
            int cnt = (r>=startt) + (g>=startt) + (b>=startt);
            if(cnt != endd[indd][i].second)return 0;
        }
    }
    if(ind == n+1){
        //cout << r << " " << g << " " << b << "\n";
        return 1;
    }
    if(dp[r][g][b]!=-1)return dp[r][g][b];

    dp[r][g][b] = ((solve(ind,g,b,ind+1) + solve(r,ind,b,ind+1))%MOD + solve(r,g,ind,ind+1))%MOD;
    return dp[r][g][b];
}

int main()
{
    si(n);si(q);
    memset(dp,-1,sizeof(dp));
    for(int i=0;i<q;i++){
        int l,r,c;
        si(l);si(r);si(c);
        endd[r].push_back({l,c});
    }
    cout << solve(0,0,0,1);
    return 0;
}