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 REP(i, N) for (int (i) = 0; (i) < (N); ++(i))
#define READALL(c) for (auto &e : c) { cin >> e; }
#define PRINTALL(c) for (const auto &e : c) { cout << e << "\t"; } cout << "\n";

template <typename T>
using V = vector<T>;

typedef long double ld;


int N, M;
vector<vector<pair<int, int>>> conds;

const int64_t MOD = 1e9+7;

int DP[305][305][305];
bool DONE[305][305][305];

int ways(int r, int b, int g) {
	if (DONE[r][b][g])
		return DP[r][b][g];
	DONE[r][b][g] = 1;
	int i = max(r, g);
	i = max(i, b);
	++i;
	bool ok = 1;
	for (const auto& cond : conds[i-1]) {
		int l, c;
		tie(l, c) = cond;
		int cc = 0;
		if (r >= l)
			++cc;
		if (b >= l)
			++cc;
		if (g >= l)
			++cc;
		if (c != cc) {
			ok = 0;
			break;
		}
	}
	if (!ok)
		return DP[r][b][g] = 0;
	if (i == N+1)
		return DP[r][b][g] = 1;
	int64_t ans = ways(i, b, g);
	ans %= MOD;
	ans += ways(r, i, g);
	ans %= MOD;
	ans += ways(r, b, i);
	ans %= MOD;
	return DP[r][b][g] = ans;

}


int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);
	cin >> N >> M;
	conds.resize(N+1);
	REP(i, M) {
		int l, r, x;
		cin >> l >> r >> x;
		conds[r].emplace_back(l, x);
	}

	cout << ways(0, 0, 0) << endl;
}