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 pb push_back
using ll = long long;
const ll mod = 1e9L + 7;

const int N = 303;

ll dp[N][N][N];

vector <pair <int, int>> lim[N];

int main() {
	ios :: sync_with_stdio(0);
	int n, m; cin >> n >> m;
	for(int i = 1; i <= m; i ++) {
		int l, r, x; cin >> l >> r >> x;
		lim[r].pb({l, x});
	}
	dp[0][0][0] = 1;
	for(int i = 0; i <= n; i ++)
		for(int j = 0; j <= i; j ++)
			for(int k = j; k <= i; k ++) {
				dp[i][j][k] %= mod;
				bool f = 1;
				for(auto p : lim[i]) {
					int l = p.first, x = p.second;
					x --;
					if(j >= l) x --;
					if(k >= l) x --;
					if(x != 0) f = 0;
				}
				if(!f) dp[i][j][k] = 0;
				dp[i + 1][j][i] += dp[i][j][k];
				dp[i + 1][k][i] += dp[i][j][k];
				dp[i + 1][j][k] += dp[i][j][k];
			}

	ll ans = 0;
	for(int i = 0; i <= n; i ++)
		for(int j = 0; j <= n; j ++) {
			//cout << i << ' ' << j << ' ' << dp[n][i][j] << '\n';
			ans += dp[n][i][j];
			ans %= mod;
		}
	cout << ans << '\n';
}