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;
const int MAX = (3e2)+2;
const long long MOD = (1e9)+7;

int n, m;
long long ans, dp[MAX][MAX][MAX];
vector<pair<int,int> > req[MAX];
int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	cin >> n >> m;
	for(int i = 0, l, r, x; i < m; i++) {
		cin >> l >> r >> x;
		req[r].emplace_back(l, x);
	}
	dp[0][0][0] = 1;
	for(int r = 0; r <= n; r++) for(int g = 0; g <= n; g++) for(int b = 0; b <= n; b++) {
		int k = max(r, max(g, b));
		for(auto p: req[k]) if((r >= p.first) + (g >= p.first) + (b >= p.first) != p.second) {
			dp[r][g][b] = 0;
			break;
		}
		if(k == n) ans = (ans + dp[r][g][b])%MOD;
		dp[k+1][g][b] = (dp[k+1][g][b] + dp[r][g][b])%MOD;
		dp[r][k+1][b] = (dp[r][k+1][b] + dp[r][g][b])%MOD;
		dp[r][g][k+1] = (dp[r][g][k+1] + dp[r][g][b])%MOD;
	}
	cout << ans;
}