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 PYTHON3):

Solution:
N,M=map(int,input().split())
Q=[[int(i) for i in input().split()] for i in range(M)]
Q.sort(key=lambda x:x[1])
mod=10**9+7
dp=[[[0]*max(1,c) for c in range(max(1,b+1))] for b in range(N+1)]
dp[0][0][0]=1
k=0
for a in range(N+1):
  check=[]
  if k<=M-1:
    while a==Q[k][1]:
      l,r,x=Q[k]
      check.append((l,r,x))
      k+=1
      if k==M:
        break
  for b in range(max(1,a)):
    for c in range(max(1,b)):
      for l,r,x in check:
        if x==1:
          if not b<l:
            dp[a][b][c]=0
            continue
        elif x==2:
          if not (b>=l and c<l):
            dp[a][b][c]=0
            continue
        elif x==3:
          if not c>=l:
            dp[a][b][c]=0
            continue
      dp[a][b][c]%=mod
      if a<=N-1:
        dp[a+1][b][c]+=dp[a][b][c]
        dp[a+1][a][c]+=dp[a][b][c]
        dp[a+1][a][b]+=dp[a][b][c]
ans=0
for b in range(N):
  for c in range(max(1,b)):
    ans+=dp[N][b][c]
    ans%=mod
print(ans)