Problem Statement

Find the number, modulo $998244353$, of integer sequences $A = (A_1, \dots, A_N)$ of length $N$ that satisfy all of the following conditions:

• $0 \leq A_i \leq M$ for all $i$ such that $1 \leq i \leq N$.
• The maximum value of $A_{L_j}, \dots, A_{R_j}$ is $X_j$ for all $j$ such that $1 \leq j \leq Q$.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq M \lt 998244353$
• $1 \leq Q \leq 2 \times 10^5$
• $1 \leq L_i \leq R_i \leq N \, (1 \leq i \leq Q)$
• $1 \leq X_i \leq M \, (1 \leq i \leq Q)$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M Q
L_1 R_1 X_1
\vdots
L_Q R_Q X_Q

Output

Print the answer.