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 <vector>
#include <algorithm>

const int P = 1000000007;

using namespace std;

vector<pair<int, int> > a[303];
int d[2][303][303];

int main() {
	int (*p)[303], (*q)[303];
	int i, j, k, l, m, n, r = 0;
	scanf("%d%d", &n, &m);
	while (m--) {
		scanf("%d%d%d", &i, &j, &k);
		a[j].emplace_back(i, k);
	}
	p = d[0];
	q = d[1];
	p[0][0] = 1;
	for (i = 0; i <= n; i++) {
		for (j = 0; j <= i; j++) for (k = 0; k <= j; k++) {
			for (auto &r : a[i]) {
				if (r.second == 1 && r.first <= j) {
					p[j][k] = 0;
					break;
				}
				if (r.second == 2 && (r.first > j || r.first <= k)) {
					p[j][k] = 0;
					break;
				}
				if (r.second == 3 && r.first > k) {
					p[j][k] = 0;
					break;
				}
			}
			if (p[j][k]) {
				if (i == n) {
					r += p[j][k];
					if (r >= P) r -= P;
					continue;
				}
				q[j][k] += p[j][k];
				if (q[j][k] >= P) q[j][k] -= P;
				q[i][k] += p[j][k];
				if (q[i][k] >= P) q[i][k] -= P;
				q[i][j] += p[j][k];
				if (q[i][j] >= P) q[i][j] -= P;
				p[j][k] = 0;
			}
		}
		swap(p, q);
	}
	printf("%d", r);
	return 0;
}