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>
#define REP(i,a,b) for(int i=(a);i<(b);i++)
#define RREP(i,a,b) for(int i=(a);i>=(b);i--)
#define pq priority_queue
#define P pair<int,int>
#define P2 pair<int,P>
#define P3 pair<int,P2>
typedef long long ll; typedef long double ld;
using namespace std;
const int INF=1e9, MOD=1e9+7, around[]={0,1,1,-1,-1,0,-1,1,0,0};
const ll LINF=1e18;
const ld PI=abs(acos(-1));
int n,m,a,b,c;
ll dp[310][310][310]; //最右のindex
vector<P> vec[310];

bool ch(int i,int j,int k){
	int r=max(i,max(j,k));
	for(auto s:vec[r]){
		if(((s.first<i)+(s.first<j)+(s.first<k))!=s.second) return 0;
	}
	
	return 1;
}

int main(){
	cin >> n >> m;
	REP(i,0,m) cin >> a >> b >> c,vec[b].push_back(P(a-1,c));
	
	dp[0][0][0]=1;
	REP(i,0,n){
		REP(j,0,n){
			REP(k,0,n){
				int ma=max(i,max(j,k));
				if(ch(i,j,ma+1)) (dp[i][j][ma+1]+=dp[i][j][k])%=MOD;
				if(ch(i,ma+1,k)) (dp[i][ma+1][k]+=dp[i][j][k])%=MOD;
				if(ch(ma+1,j,k)) (dp[ma+1][j][k]+=dp[i][j][k])%=MOD;
			}
		}
	}
	
	ll s=0;
	REP(i,0,n+1){
		REP(j,0,n+1){
			s+=dp[n][i][j];
			s+=dp[i][n][j];
			s+=dp[i][j][n];
		}
	}
	cout << s%MOD << endl;
	return 0;
}