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;
int dp[305][305][305], n;
vector<pair<int, int>> a[305];
int yo(int i, int r, int g, int b) {
	int &ret = dp[r][g][b];
	if (ret != -1) return ret;
	for (auto x: a[i - 1]) {
		int l = x.first;
		int cnt = (l <= r) + (l <= g) + (l <= b);
		if (cnt != x.second) return ret = 0;
	}
	if (i == n + 1) return 1;
	ret = yo(i + 1, i, g, b) + yo(i + 1, r, i, b);
	if (ret >= mod) ret -= mod;
	ret += yo(i + 1, r, g, i);
	if (ret >= mod) ret -= mod;
	return ret;
}
int32_t main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int m; cin >> n >> m;
	while (m--) {
		int l, r, k; cin >> l >> r >> k;
		a[r].push_back({l, k});
	}
	memset(dp, -1, sizeof dp);
	cout << yo(1, 0, 0, 0) << '\n';
    return 0;
}