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 pii pair<int,int>
#define ll long long
vector<pii> lim[305];
ll dp[305][305][305],n,m;
const ll md=1000000007;
inline ll dfs(int x,int r,int g,int b){
	if(~dp[r][g][b])return dp[r][g][b];
	dp[r][g][b]=0;
	if(x>0)for(int i=0;i<lim[x-1].size();++i){
		int l=lim[x-1][i].first,k=lim[x-1][i].second;
		int c=(bool)(r>=l)+(bool)(g>=l)+(bool)(b>=l);
		if(c!=k)return 0;
	}
	if(x==n+1){
		dp[r][g][b]=1;
		return 1;
	}
	dp[r][g][b]=(dfs(x+1,x,g,b)+dfs(x+1,r,x,b)+dfs(x+1,r,g,x))%md;
	return dp[r][g][b];
}
int main(){
	ios_base::sync_with_stdio(false);
	cin>>n>>m;
	for(int i=1,l,r,x;i<=m;++i){
		cin>>l>>r>>x;
		lim[r].push_back({l,x});
	}
	memset(dp,-1,sizeof(dp));
	cout<<dfs(1,0,0,0)<<'\n';
}