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>
#define MOD 1000000007
using namespace std;
const int N = 303;
int dp[N][N][N];
int n,m;
struct cond{
    int l,r, x;
};

vector<vector<cond> > vec(N);

bool check(int ind,int rd,int g ,int b) {
    for(int i = 0;i<vec[ind].size();i++) {
        int l = vec[ind][i].l, r = vec[ind][i].r, x = vec[ind][i].x;
        int cnt = (rd >= l && rd <= r) + (b >= l && b <= r) + (g >= l && g <= r);
        if(cnt != x)
            return false;
    }
    return true;
}

int solve(int r,int g,int b) {
    int ind = max(r,max(g,b));
    if(!check(ind,r,g,b))
        return 0;
    if(ind == n)
        return 1;
    if(dp[r][g][b] != -1)
        return dp[r][g][b];
    return dp[r][g][b] = ((solve(ind+1,g,b) + solve(r,ind+1,b)) % MOD + solve(r,g,ind+1) ) % MOD;
}


int main()
{
    scanf("%d%d",&n,&m);
    for(int i = 0;i<m;i++) {
        int l,r,x;
        scanf("%d%d%d",&l,&r,&x);
        vec[r].push_back(cond{l,r,x});
    }
    memset(dp,-1,sizeof dp);
    printf("%d",solve(0,0,0));
    return 0;
}