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>

const int N = 305, mod = 1000000007;

std::vector<std::pair<int, int>> v[N];

int dp[N][N][N], ans, n, m;

void up(int &x, int y) { x += y - mod, x += x >> 31 & mod; }
void check(int i) {
	for (int j = 0; j <= i; ++j)
		for (int k = 0; k <= j; ++k) {
			for (auto p : v[i])
				if ((j >= p.first) + (k >= p.first) != p.second)
					{dp[i][j][k] = 0; break;}
		}
}

int main() {
	std::ios::sync_with_stdio(0), std::cin.tie(0);
	std::cin >> n >> m;
	for (int i = 0, l, r, x; i < m; ++i)
		std::cin >> l >> r >> x, v[r].emplace_back(l, x - 1);
	dp[0][0][0] = 1;
	for (int i = 0; i < n; check(++i)) {
		for (int j = 0; j <= i; ++j)
			for (int k = 0; k <= j; ++k) {
				up(dp[i + 1][j][k], dp[i][j][k]);
				up(dp[i + 1][i][k], dp[i][j][k]);
				up(dp[i + 1][i][j], dp[i][j][k]);
			}
	}
	for (int i = 0; i <= n; ++i)
		for (int j = 0; j <= i; ++j)
			up(ans, dp[n][i][j]);
	std::cout << ans << '\n';
	return 0;
}