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 fst first
#define snd second
#define fore(i,a,b) for(int i=a,ThxDem=b;i<ThxDem;++i)
#define pb push_back
#define ALL(s) s.begin(),s.end()
#define FIN ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)
#define SZ(s) int(s.size())
using namespace std;
typedef long long ll;
typedef pair<int,int> ii;

int MOD=1e9+7, n,dp[310][310][310];
int mx[310][4],mn[310][4];

int solve(int i, int j, int k){	//R=i, G=j, B=k
	int &r=dp[i][j][k];
	if(r>=0) return r;
	int now=max({i,j,k});
	if(now==n+1) return r=1;
	int low=min({i,j,k}), mid=low^now^i^j^k;
	int can=1;
	if(mx[now][1]>=0) can&=mn[now][1]>mid&&mx[now][1]<=now;
	if(mx[now][2]>=0) can&=mn[now][2]>low&&mx[now][2]<=mid;
	if(mx[now][3]>=0) can&=mx[now][3]<=low;
	r=0;
	if(can){
		r+=solve(now+1,j,k); if(r>=MOD)r-=MOD;
		r+=solve(i,now+1,k); if(r>=MOD)r-=MOD;
		r+=solve(i,j,now+1); if(r>=MOD)r-=MOD;
	}
	return r;
}

int main(){FIN;
	memset(dp,-1,sizeof(dp));
	int q; cin>>n>>q;
	fore(i,0,n+1) fore(j,0,4) mx[i][j]=-1e9,mn[i][j]=1e9;
	while(q--){
		int l,r,x; cin>>l>>r>>x;
		mn[r][x]=min(mn[r][x],l);
		mx[r][x]=max(mx[r][x],l);
	}
	cout << solve(0,0,0)*333333336ll%MOD << "\n";
}