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 pb push_back
#define fst first
#define snd second
#define fore(i,a,b) for(int i=a,ggdem=b;i<ggdem;++i)
#define SZ(x) ((int)x.size())
#define ALL(x) x.begin(),x.end()
#define mset(a,v) memset((a),(v),sizeof(a))
#define FIN ios::sync_with_stdio(0);cin.tie(0);cout.tie(0)
using namespace std;
typedef long long ll;

ll n;
ll MOD=1e9+7;
vector<pair<ll,ll>> g[303];
ll dp[303][303][303];

ll f(ll x, ll y, ll z){
	ll &r=dp[x][y][z];
	if(r>=0)return r;
	ll m=max({x,y,z});
	if(m==n+1){
		r=333333336; return r;
	}
	for(auto i:g[m]){
		ll tot=(x>=i.fst)+(y>=i.fst)+(z>=i.fst);
		if(tot!=i.snd){
			r=0; return r;
		}
	}
	/*r=(f(m+1,y,z)+f(x,m+1,z));
	if(r>=MOD)r-=MOD;
	r+=+f(x,y,m+1);
	if(r>=MOD)r-=MOD;*/
	r=(f(m+1,y,z)+f(x,m+1,z)+f(x,y,m+1))%MOD;
	return r;
}

int main(){FIN;
	ll m; cin>>n>>m;
	pair<pair<ll,ll>,ll> a[m];
	fore(i,0,m)cin>>a[i].fst.fst>>a[i].fst.snd>>a[i].snd;
	fore(i,0,m){
		g[a[i].fst.snd].pb({a[i].fst.fst,a[i].snd});
	}
	mset(dp,-1);
	cout<<f(0,0,0);
	
	return 0;
}