RGB Sequence

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

inputFormat

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

outputFormat

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

样例

3 1
1 3 3

6