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;

using ll = long long;
ll n;
ll m;
ll dp[305][305][305];
const ll MOD = 1e9+7;

vector<pair<int, int>> v[305];

bool check(int r, int g, int b) 
{
	int k = max({r, b, g});
	for(auto pp: v[k]) 
	{
    	int ct = 0;
    	int l = pp.first;
    	if (r >= l) ct++;
    	if (g >= l) ct++;
    	if (b >= l) ct++;
    
    	if (ct != pp.second) return false;
	}
	return true;
}
 
int main() 
{
	ios::sync_with_stdio(false);
	cin.tie(0); 

	cin>>n>>m;
	for (int i=0;i<m;++i)
	{
		int l,r,x;
		cin>>l>>r>>x;
		v[r].push_back({l,x});
	}  
	dp[0][0][0]=1;
	ll ret=0;
	for (int r=0;r<=n;++r)
	{
		for (int g=0;g<=n;++g)
		{
			for (int b=0;b<=n;++b)
			{
				ll c=dp[r][g][b];
				if (!c) continue;
				
				if (!check(r,g,b))
				{
					dp[r][g][b]=0;
					continue;
				}
				
				int k=max({r,g,b}) + 1;
				if (k-1 == n)
				{
					ret+=dp[r][g][b];
					ret%=MOD;
				}
				dp[k][g][b]+=dp[r][g][b] % MOD;
				dp[r][k][b]+=dp[r][g][b] % MOD;
				dp[r][g][k]+=dp[r][g][b] % MOD;
				
			}
		}
	}
	cout<<ret;
 
}