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 mod = 1e9 + 7;
const int MAXN = 3e2 + 10;

int n, m, dp[MAXN][MAXN][MAXN];
vector<pair<int, int> > lim[MAXN];

inline bool check(int r, int g, int b) {
	int k = max(r, max(g, b));
	for (int j = 0; j < lim[k].size(); ++j) {
		int l = lim[k][j].first, x = lim[k][j].second, cnt;
		cnt = (r >= l) + (g >= l) + (b >= l);
		if (cnt != x) return 0;
	}
	return 1;
}

int main() {
	scanf("%d%d", &n, &m);
	for (int i = 0; i < m; ++i) {
		int l, r, x;
		scanf("%d%d%d", &l, &r, &x);
		lim[r].push_back(make_pair(l, x));
	}
	memset(dp, 0, sizeof dp);
	dp[0][0][0] = 1;
	int ans = 0;
	for (int i = 0; i <= n; ++i)
		for (int j = 0; j <= n; ++j)
			for (int k = 0; k <= n; ++k) {
				if (!dp[i][j][k]) continue;
				if (!check(i, j, k)) {
					dp[i][j][k] = 0;
					continue;
				}
				int len = max(i, max(j, k)) + 1;
				if (len == n + 1)
					(ans += dp[i][j][k]) %= mod;
				(dp[len][j][k] += dp[i][j][k]) %= mod;
				(dp[i][len][k] += dp[i][j][k]) %= mod;
				(dp[i][j][len] += dp[i][j][k]) %= mod;
			}
	printf("%d\n", ans);
}