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 rep(i,n) for(int i=0; i<(n); i++)
using P = pair<int,int>;
const int MOD = 1e9+7;
int n, m, l, r, x;
long long dp[305][305] = {1}, ans;
vector<P> p[305];
int main(){
	cin >> n >> m;
	rep(i,m){
		cin >> l >> r >> x;
		p[r-1].push_back(P(l,x));
	}
	rep(i,n){
		rep(j,i) rep(k,i) (dp[i][j] += dp[max(j,k)][min(j,k)]) %= MOD;
		for(P t: p[i]){
			tie(l,x) = t;
			rep(j,i+1) rep(k,j+1) if(x+(j<l)+(k<l)-3) dp[j][k] = 0;
		}
	}
	rep(i,n) rep(j,i) (ans += 6*dp[i][j]) %= MOD;
	cout << (ans + dp[0][0]*3) % MOD;
}