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 <cstring>
#include <algorithm>
using namespace std;

#define iter(i, n) for (int i = 1; i <= n; ++i)
#define NR 310

const int mod = 1e9 + 7;

int L[NR][4], R[NR][4], n, m, f[NR][NR][NR];

bool valid(int i, int j, int k) {
	if (i > j) swap(i, j);
	if (j > k) swap(j, k);
	if (i > j) swap(i, j);

	if (k == 0) return true;

	return j + 1 <= L[k][1] &&
		i + 1 <= L[k][2] && R[k][2] <= j && 
		R[k][3] <= i;
}

int dfs(int i, int j, int k) {
//	printf("!%d %d %d\n", i, j, k);
	if (!valid(i, j, k)) return 0;
	int &w = f[i][j][k];
	if (w != -1) return w;
	int s = max(i, max(j, k));
	if (s == n) return 1;
	w = (0ll + dfs(s + 1, j, k) + dfs(i, s + 1, k) + dfs(i, j, s + 1)) % mod;
	return w;
}

int main() {
	memset(f, -1, sizeof(f));
	scanf("%d%d", &n, &m);
	iter(i, n) iter(j, 3) L[i][j] = n;
	iter(i, m) {
		int l, r, x;
		scanf("%d%d%d", &l, &r, &x);
		L[r][x] = min(L[r][x], l);
		R[r][x] = max(R[r][x], l);
	}
	printf("%d\n", dfs(0, 0, 0));
	return 0;
}