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 <stdio.h>
#include <iostream>
#include <algorithm>
#include <memory.h>
#include <vector>

using namespace std;
typedef long long LL;
typedef pair<int,int> mp;
#define pb push_back
const int maxn = 305;
const int mod = 1e9+7;

int dp[maxn][maxn][maxn],n,m,ans;
vector<mp> lim[maxn];
int main()
{
	#ifdef Amberframe
		freopen("arc074e.in","r",stdin);
		freopen("arc074e.out","w",stdout);
	#endif
	scanf("%d %d",&n,&m);dp[0][0][0]=1;
	for (int l,r,x,i=1;i<=m;i++)
		scanf("%d %d %d",&l,&r,&x),lim[r].pb(mp(l,x));
	for (int i=0;i<=n;i++)
	for (int j=0;j<=n;j++)
	for (int k=0;k<=n;k++)
	if (int w=dp[i][j][k]) {
		int t=max(max(i,j),k);bool tag=true;
		for (unsigned l=0;l<lim[t].size();l++)
		{
			int u=lim[t][l].first,s=lim[t][l].second;
			tag&=((i>=u)+(j>=u)+(k>=u))==s;
		}
		if (!tag) continue;
		if (t==n) (ans+=w)%=mod;
		(dp[t+1][j][k]+=w)%=mod;
		(dp[i][t+1][k]+=w)%=mod;
		(dp[i][j][t+1]+=w)%=mod;
	}
	printf("%d",ans);
	return 0;
}