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 N = 310, mod = 1e9 + 7;

int dp[N][N][N];

inline void Inc(int &x, int y) {
	x += y, x -= x >= mod ? mod : 0;
}

typedef pair<int, int> P;

vector<P> q[N];

int main() {
	int n, m, res = 0; scanf("%d%d", &n, &m);
	for (int i = 1, l, r, a; i <= m; i++)
		scanf("%d%d%d", &l, &r, &a), q[r].push_back(P(l, a));
	dp[0][0][0] = 1;
	for (int i = 0; i <= n; i++)
		for (int j = 0; j <= i; j++)
			for (int k = 0; k <= j; k++) if (dp[i][j][k]) {
				bool flg = true;
				for (auto v : q[i]) {
					int c = 1;
					if (j >= v.first) c++;
					if (k >= v.first) c++;
					if (v.second != c) {
						flg = false; break;
					}
				}
				if (!flg) continue;
				Inc(dp[i + 1][j][k], dp[i][j][k]), Inc(dp[i + 1][i][k], dp[i][j][k]), Inc(dp[i + 1][i][j], dp[i][j][k]);
				if (i == n) Inc(res, dp[i][j][k]);
			}
	printf("%d\n", res);
}