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<cstring>
#include<algorithm>
#include<vector>
using namespace std;
typedef pair<int,int> P;

const int maxn = 309;
const int MOD = 1000000007;
int f[maxn][maxn][maxn];
vector<P> q[maxn];
int n, m, l, r, x, p, ans;

bool check(int r, int R, int G, int B){
	int l, x, cnt;
	for (int i=q[r].size()-1; i>=0; i--){
		l = q[r][i].first; x = q[r][i].second;
		cnt = (l <= R);
		cnt += (l <= G);
		cnt += (l <= B);
		if (cnt != x) return false;
	}
	return true;
}

int main(){
	scanf("%d%d", &n, &m);
	for (int i=1; i<=m; i++){
		scanf("%d%d%d", &l, &r, &x);
		q[r].push_back(make_pair(l, x));
	}
	f[0][0][0] = 1;
	for (int i=0; i<=n; i++)
		for (int j=0; j<=n; j++)
			for (int k=0; k<=n; k++){
				p = max(i, max(j, k));
				if (!check(p, i, j, k)) continue;
				if (p == n) ans = (ans + f[i][j][k]) % MOD;
				f[p+1][j][k] = (f[p+1][j][k] + f[i][j][k]) % MOD;
				f[i][p+1][k] = (f[i][p+1][k] + f[i][j][k]) % MOD;
				f[i][j][p+1] = (f[i][j][p+1] + f[i][j][k]) % MOD;
			}
	printf("%d\n", ans);
	return 0;
}