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 rep(i,a,b) for(int i=(a),i##_end=(b);i<=i##_end;i++)
#define per(i,a,b) for(int i=(b),i##_st=(a);i>=i##_st;i--)
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define dbg(x) cerr<<#x" = "<<x<<endl
#define debug(...) fprintf(stderr, __VA_ARGS__)
#define Es(x,i) for(Edge *i=G[x];i;i=i->nxt)
typedef long long ll;
typedef pair<int,int> pii;
const int inf=~0u>>1,MOD=1e9+7;
inline int rd() {
    int x,c,f=1;while(!isdigit(c=getchar()))f=c!='-';x=c-'0';
    while(isdigit(c=getchar()))x=x*10+c-'0';return f?x:-x;
}
const int N=305;
inline void add(int&x,int y){(x+=y)%=MOD;}
int n,m,f[N][N],ans;
vector<pii>v[N];
inline bool jud(int i,int j,int k){for(pii x:v[i])if((j>=x.fi)+(k>=x.fi)+1!=x.se)return 0;return 1;}
int main(){
	n=rd(),m=rd();
	rep(i,1,m){int l=rd(),r=rd(),x=rd();v[r].pb(mp(l,x));}
	f[0][0]=1;
	rep(i,1,n)per(j,0,i)per(k,0,j)if(jud(i,j,k)){
		add(f[i][k],f[j][k]),add(f[i][j],f[j][k]);
	} else f[j][k]=0;
	int ans=0;rep(i,0,n)rep(j,0,i)add(ans,f[i][j]);
	cout<<ans<<endl;
}