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;
const int maxn=302,p=1e9+7;
int f[maxn][maxn][maxn],n,m;
vector<pair<int,int> >s[maxn];
void add(int &x,int y){x+=y;if(x>p) x-=p;}
int check(int r,int g,int b){
    int now=max(r,max(g,b));
    for(int i=0;i<s[now].size();++i){
        int l=s[now][i].first,x=s[now][i].second;
        int p=(r>=l)+(g>=l)+(b>=l);
        if(p!=x)return 1;
    }
	return 0;
}
int main(){
	cin>>n>>m;
    for(int i=1,l,r,x;i<=m;++i)cin>>l>>r>>x,s[r].push_back(make_pair(l,x));
    f[0][0][0]=1;int ans=0;
    for(int r=0;r<=n;++r)
        for(int g=0;g<=n;++g)
            for(int b=0;b<=n;++b){
                if((r==g||r==b||g==b)&&((!r)+(!g)+(!b))<2)continue;
                if(check(r,g,b))continue;
                int k=max(r,max(g,b))+1;
                add(f[k][g][b],f[r][g][b]);
                add(f[r][k][b],f[r][g][b]);
                add(f[r][g][k],f[r][g][b]);
                if(k==n+1)add(ans,f[r][g][b]);
		}
		cout<<ans;
}