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 <vector>
#include <algorithm>
const int MOD = 1000000007;
int N, M, f[301][301][301];
std::vector < std::pair < int, int > > V[301];
inline void add(int &x, int y)
{
	x = x + y < MOD ? x + y : x + y - MOD;
}
int main()
{
	scanf("%d%d", &N, &M);
	while (M--)
	{
		int l, r, t;
		scanf("%d%d%d", &l, &r, &t);
		V[r].push_back({ l, t });
	}
	f[0][0][0] = 1;
	for (int i = 0; i < N; i++)
		for (int j = 0; j <= i; j++)
			for (int k = j; k <= i; k++)
			{
				bool check = true;
				for (auto &e : V[i])
					if (1 + (j >= e.first) + (k >= e.first) != e.second)
						check = false;
				if (check)
				{
					add(f[i + 1][j][k], f[i][j][k]);
					add(f[i + 1][j][i], f[i][j][k]);
					add(f[i + 1][k][i], f[i][j][k]);
				}
			}
	int O = 0;
	for (int i = 0; i <= N; i++)
		for (int j = 0; j <= N; j++)
		{
			bool check = true;
			for (auto &e : V[N])
				if (1 + (i >= e.first) + (j >= e.first) != e.second)
					check = false;
			if (check)
				add(O, f[N][i][j]);
		}
	printf("%d\n", O);
	return 0;
}