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>
#define fi first
#define se second
#define mp make_pair
using namespace std;

const int mod = 1000000007;

typedef pair <int, int> pii;

vector <pii> from[310];
int f[310][310][310];

bool alive(int a, int b, int c) {
	for (int i = 0; i < from[a].size(); i++) {
		int l = from[a][i].fi, x = from[a][i].se;
		int xx = l > b ? 1 : l > c ? 2 : 3;
		if (xx != x) return 0;
	}
	return 1;
}

void add(int &a, int b) {
	a += b;
	if (a >= mod) a -= mod;
}

int main () {
	int n, m; scanf("%d%d", &n, &m);
	for (int i = 0; i < m; i++) {
		int l, r, x; scanf("%d%d%d", &l, &r, &x);
		from[r].push_back(mp(l, x));
	}
	f[0][0][0] = 1;
	long long ans = 0;
	for (int i = 0; i <= n; i++) {
		for (int j = 0; j <= i; j++) {
			for (int k = 0; k <= j; k++) {
				if (!f[i][j][k]) continue;
				if (alive(i, j, k)) {
					if (i == n) ans = (ans + f[i][j][k]) % mod;
					else {
						add(f[i + 1][j][k], f[i][j][k]);
						add(f[i + 1][i][k], f[i][j][k]);
						add(f[i + 1][i][j], f[i][j][k]);
					}
				}
			}
		}
	}
	printf("%lld\n", ans);
	return 0;
}