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;

using pii = pair<int, int>;
#define X first
#define Y second

const int N = 305, M = int(1e9) + 7;

int n, m, d[N][N][N];
bool c[N][N][N];
vector<pii> v[N];

int f(int x, int y, int z){
	if(c[x][y][z]) return d[x][y][z];
	c[x][y][z] = 1;
	for(pii i : v[x]){
		if((i.Y == 1 && y < i.X) ||
			(i.Y == 2 && y >= i.X && z < i.X) ||
			(i.Y == 3 && z >= i.X)) continue;
		return 0;
	}
	if(x == n) d[x][y][z] = 1;
	else d[x][y][z] = ((f(x + 1, y, z) + f(x + 1, x, z)) % M + f(x + 1, x, y)) % M;
	return d[x][y][z];
}

int main(){
	ios_base::sync_with_stdio(false); cin.tie(NULL);
	cin >> n >> m;
	for(int x, y, z; m--; ){
		cin >> x >> y >> z;
		v[y].emplace_back(x, z);
	}
	cout << (3LL * f(1, 0, 0) % M) << endl;
}