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;
typedef long long ll;
typedef unsigned long long ull;
#define FOR(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define rep(i, n) FOR(i, 0, n)

const int MaxN = 300, MaxM = 300;
const int Mod = (int)1e9 + 7;
int N, M;
int dp[MaxN + 1][MaxN + 1][MaxN + 1];
vector<pair<int, int>> Q[MaxN + 1];

bool OK(int a, int b, int c, int last) {
	for (auto q : Q[last]) {
		int cnt = (a >= q.first && a <= last) + (b >= q.first && b <= last) + (c >= q.first && c <= last);
		if (cnt != q.second) return false;
	}
	return true;
}

void solve() {
	dp[0][0][0] = 1;
	int ans = 0, val;
	rep(a, N + 1) rep(b, N + 1) rep(c, N + 1) if ((val = dp[a][b][c]) > 0) {
		int last = max(a, max(b, c));
		if (!OK(a, b, c, last)) continue;
		if (last == N) { (ans += val) %= Mod; continue; }
		(dp[last + 1][b][c] += val) %= Mod;
		(dp[a][last + 1][c] += val) %= Mod;
		(dp[a][b][last + 1] += val) %= Mod;
	}
	cout << ans << endl;
}

int main() {
	cin >> N >> M;
	rep(i, M) {
		int L, R, x;
		cin >> L >> R >> x;
		Q[R].push_back(make_pair(L, x));
	}
	solve();
	return 0;
}