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 ll long long
#define mp make_pair
#define pb push_back

#define eprintf(...) fprintf(stderr, __VA_ARGS__)
#define rep(i, n) for (int i = 0; i < (int)(n); ++ i)

const int mod = 1e9 + 7;
int n, q;
vector <pair <int, int> > lim[305];
int dp[305][305][305];

int f(int i, int a, int b, int c) {
	if (~dp[a][b][c]) return dp[a][b][c];
	rep(j, lim[i].size()) {
		int l = lim[i][j].first, x = lim[i][j].second;
		int cnt = (a >= l) + (b >= l) + (c >= l);
		if (cnt != x) return dp[a][b][c] = 0;
	}
	if (i == n) return dp[a][b][c] = 1;
	return dp[a][b][c] = (0LL + f(i + 1, i + 1, b, c) + f(i + 1, a, i + 1, c) + f(i + 1, a, b, i + 1)) % mod;
}

int main() {
	scanf("%d %d", &n, &q);
	rep(i, q) {
		int l, r, x;
		scanf("%d %d %d", &l, &r, &x);
		lim[r].pb(mp(l, x));
	}
	memset(dp, -1, sizeof(dp));
	printf("%d\n", f(0, 0, 0, 0));
	return 0;
}