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 <cstdio>
#include <cstring>
#include <iostream>
#include <cmath>
#include <algorithm>
#include <vector>

using namespace std;

const int mod = 1000000007;
int N;
int dp[305][305][305];
vector<int> ed[305][4];
int m;

bool chk(int x,int y,int z)
{
	int maxn = 0;
	for(auto i : ed[x][1])
		if(i <= y) return false;
	for(auto i : ed[x][2])
		if(i <= z || i > y) return false;
	for(auto i : ed[x][3])
		if(i > z) return false;
	return true;
}

int main()
{
	scanf("%d%d",&N,&m);
	for(int i = 1;i <= m; ++ i)
	{
		int l,r,c; scanf("%d%d%d",&l,&r,&c);
		ed[r][c].push_back(l);
	}
	for(int i = 1;i <= N; ++ i)
		for(int j = 1;j <= 3; ++ j)
			sort(ed[i][j].begin(),ed[i][j].end());
	dp[0][0][0] = 1;
	long long ans = 0;
	for(int i = 0;i <= N; ++ i)
		for(int j = 0;j <= i; ++ j)
			for(int k = 0;k <= j; ++ k)
			{
				if(!chk(i,j,k)) dp[i][j][k] = 0;
				if(i == N) ans = (ans + dp[i][j][k]) % mod;
				dp[i + 1][j][k] += dp[i][j][k];
				dp[i + 1][i][k] += dp[i][j][k];
				dp[i + 1][i][j] += dp[i][j][k];
				dp[i + 1][j][k] %= mod;
				dp[i + 1][i][k] %= mod;
				dp[i + 1][i][j] %= mod;
			}
	printf("%lld\n",ans);
}