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>
typedef long long ll;
#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define REP(i,a) FOR(i,0,a)
	
using namespace std;
const int MAX_N=300;
int N,M;
const ll MOD=1e9+7;
typedef pair<int,int> P;
vector<P> con[MAX_N+1];
ll dp[MAX_N+1][MAX_N+1][MAX_N+1];
ll dfs(int i,int r,int g,int b){
	if (dp[r][g][b]!=-1){
		return dp[r][g][b];
	}
	ll ret=0;
	REP(j,(int)con[i-1].size()){
		P p=con[i-1][j];
		int cnt=0;
		if (p.first<=r){
			cnt++;
		}
		if (p.first<=g){
			cnt++;
		}
		if (p.first<=b){
			cnt++;
		}
		if (cnt!=p.second){
			return dp[r][g][b]=0;
		}
	}
	if (i==N+1){
		return dp[r][g][b]=1;
	}
	ret=dfs(i+1,i,g,b);
	ret%=MOD;
	ret+=dfs(i+1,r,i,b);
	ret%=MOD;
	ret+=dfs(i+1,r,g,i);
	ret%=MOD;
	return dp[r][g][b]=ret;
}
int main(){
	cin>>N>>M;
	REP(i,M){
		int l,r,x;
		cin>>l>>r>>x;
		con[r].push_back(P(l,x));
	}
	memset(dp,-1,sizeof(dp));
	cout<<dfs(1,0,0,0)<<endl;
	return 0;
}