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:
/*  Bismillahir Rahmanir Rahim  */

#include <bits/stdc++.h>

using namespace std;

const int N = 305;
const long long mod = 1e9 + 7;

int dp[N][N][N];
int ck[N][2][4];
int n, m;

bool ok(int a, int b, int c){
	int at = max({a, b, c});
	for(int j = 0; j <= 1; ++j){
		for(int i = 1; i <= 3; ++i){
			if(ck[at][j][i] == 0) continue;
			int cnt = 0;
			cnt += (a >= ck[at][j][i]);
			cnt += (b >= ck[at][j][i]);
			cnt += (c >= ck[at][j][i]);
			if(cnt != i) return false;
		}
	}
	return true;
}

int recur(int l1, int l2, int l3){
	int at = max({l1, l2, l3}) + 1;
	if(at == n + 1) return 1;
	if(dp[l1][l2][l3] != -1) return dp[l1][l2][l3];
	long long ret = 0;
	if(ok(at, l2, l3)) ret += recur(at, l2, l3);
	if(ok(l1, at, l3)) ret += recur(l1, at, l3);
	if(ok(l1, l2, at)) ret += recur(l1, l2, at);
	return dp[l1][l2][l3] = ret % mod;
}

int main(){
	int l, r, x;
	scanf("%d %d", &n, &m);
	for(int i = 1; i <= m; ++i){
		scanf("%d %d %d", &l, &r, &x);
		if(ck[r][0][x] == 0){
			ck[r][0][x] = l; 
			ck[r][1][x] = l;
		}
		else{ 
			ck[r][0][x] = min(ck[r][0][x], l);
			ck[r][1][x] = max(ck[r][1][x], l);
		}
	}
	memset(dp, -1, sizeof(dp));
	printf("%d\n", recur(0, 0, 0));
	return 0;
}