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.

-----Sample Input-----
3 1
1 3 3

-----Sample Output-----
6

The six ways are:
- RGB
- RBG
- GRB
- GBR
- BRG
- BGR
where R, G and B correspond to red, green and blue squares, respectively.

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