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;


#define int long long 


const int N = 303, mod = 1e9 + 7;

vector <pair <int, int> > L[N];


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


int chk(int pos, int r, int g, int b) {
	for(auto z: L[pos]) {
		int c = (z.first <= r) + (z.first <= g) + (z.first <= b);
		if(c != z.second) {
			return 0;
		}
	}
	return 1;
}

int f(int r, int g, int b) {
	int pos = max({r, g, b}) + 1;
	if(pos > n) {
		return 1;
	}
	if(~dp[r][g][b]) {
		return dp[r][g][b];
	}
	int res = 0;
	if(chk(pos, pos, g, b)) {
		res += f(pos, g, b);
	}
	if(chk(pos, r, pos, b)) {
		res += f(r, pos, b);
	}
	if(chk(pos, r, g, pos)) {
		res += f(r, g, pos);
	}
	return dp[r][g][b] = res % mod;
}

int32_t main() {
	ios_base :: sync_with_stdio(0); cin.tie(0); cout.tie(0);
	int m; cin >> n >> m;
	for(int i = 1; i <= m; i++) {
		int l, r, x; cin >> l >> r >> x;
		L[r].push_back(make_pair(l, x));
	}
	memset(dp, -1, sizeof dp);
	cout << f(0, 0, 0) << endl;
}