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 <cstdio>
#include <algorithm>
#include <cstring>
#include <iostream>
#include <vector>

#define For(i, j, k) for(int i = j; i <= k; i++)
#define Forr(i, j, k) for(int i = j; i >= k; i--)
#define pb push_back

using namespace std;

const int N = 310;
const int Mod = 1e9 + 7;

struct Constraint{
	int l, x;
};

vector<Constraint> C[N];

inline void add(int &x, int y){
	x += y;
	if(x >= Mod) x -= Mod;
}

int n, m;
int dp[N][N][N];

int main(){
	scanf("%d%d", &n, &m);
	For(i, 1, m){
		int l, r, x;
		scanf("%d%d%d", &l, &r, &x);
		C[r].pb((Constraint){l, x});
	}
	dp[0][0][0] = 1;
	For(i, 0, n - 1){
		For(a, 0, i) For(b, 0, i){
			int v = dp[i][a][b];
			if(!v) continue;
			add(dp[i + 1][a][b], v);
			add(dp[i + 1][a][i], v);
			add(dp[i + 1][b][i], v);
		}

		For(a, 0, i + 1) For(b, 0, i + 1){
			bool valid = true;
			for(auto v : C[i + 1])
				if((a >= v.l) + (b >= v.l) != v.x - 1){
					valid = false;
					break;
				}
			if(!valid) dp[i + 1][a][b] = 0;
		}
	}
	
	int ans = 0;
	For(i, 0, n) For(j, 0, n) add(ans, dp[n][i][j]);
	printf("%d\n", ans);

	return 0;
}