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<vector>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
#define ll long long
#define mod 1000000007LL

struct node { ll l,x; };
vector<node> v[310];

ll f[310][310][310],n,m,ans;

inline ll rd()
{
	ll x=0;char ch=getchar();
	for (;ch<'0'||ch>'9';ch=getchar());
	for (;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0';
	return x;
}

inline bool check(ll r,ll g,ll b)
{
	ll x=max(max(r,g),b);
	for (ll siz=v[x].size(),i=0;i<siz;i++)
	{
		ll l=v[x][i].l,hh=v[x][i].x,hhh=0;
		if (r>=l) hhh++;
		if (g>=l) hhh++;
		if (b>=l) hhh++;
		if (hh!=hhh) return false;
	}
	return true;
}

int main()
{
	n=rd();m=rd();
	for (ll i=1;i<=m;i++)
	{
		ll l=rd(),r=rd(),x=rd();
		v[r].push_back((node){l,x});
	}
	f[0][0][0]=1LL;ans=0LL;
	for (ll r=0;r<=n;r++) for (ll g=0;g<=n;g++) for (ll b=0;b<=n;b++)
	{
		if (!f[r][g][b]) continue;
		if (!check(r,g,b)) continue;
		ll x=max(max(r,g),b)+1;
		if (x==n+1) { ans=(ans+f[r][g][b])%mod;continue; }
		f[x][g][b]+=f[r][g][b]%mod;
		f[r][x][b]+=f[r][g][b]%mod;
		f[r][g][x]+=f[r][g][b]%mod;
	}
	printf("%lld\n",ans);
	return 0;
}