Problem Statement

Print the number of sequences $a$ that are permutations of $(1, 2, 3, \dots, N)$ and satisfy the following condition:

• for every integer $i$ such that $1 \le i \le M$, at most $Z_i$ numbers among $a_1, a_2, a_3, \dots, a_{X_i}$ are less than or equal to $Y_i$ .

Constraints

• $2 \le N \le 18$
• $0 \le M \le 100$
• $1 \le X_i \lt N$
• $1 \le Y_i \lt N$
• $0 \le Z_i \lt N$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
X_1 Y_1 Z_1
X_2 Y_2 Z_2
X_3 Y_3 Z_3
\hspace{23pt} \vdots
X_M Y_M Z_M

Output

Print the answer.