You are given three integers $$$n$$$, $$$k$$$, $$$m$$$ and $$$m$$$ conditions $$$(l_1, r_1, x_1), (l_2, r_2, x_2), \dots, (l_m, r_m, x_m)$$$.
Calculate the number of distinct arrays $$$a$$$, consisting of $$$n$$$ integers such that:
Two arrays $$$a$$$ and $$$b$$$ are considered different if there exists such a position $$$i$$$ that $$$a_i \neq b_i$$$.
The number can be pretty large so print it modulo $$$998244353$$$.
The first line contains three integers $$$n$$$, $$$k$$$ and $$$m$$$ ($$$1 \le n \le 5 \cdot 10^5$$$, $$$1 \le k \le 30$$$, $$$0 \le m \le 5 \cdot 10^5$$$) — the length of the array $$$a$$$, the value such that all numbers in $$$a$$$ should be smaller than $$$2^k$$$ and the number of conditions, respectively.
Each of the next $$$m$$$ lines contains the description of a condition $$$l_i$$$, $$$r_i$$$ and $$$x_i$$$ ($$$1 \le l_i \le r_i \le n$$$, $$$0 \le x_i < 2^k$$$) — the borders of the condition segment and the required bitwise AND value on it.
Print a single integer — the number of distinct arrays $$$a$$$ that satisfy all the above conditions modulo $$$998244353$$$.
4 3 2 1 3 3 3 4 6
3
5 2 3 1 3 2 2 5 0 3 3 3
33
You can recall what is a bitwise AND operation here.
In the first example, the answer is the following arrays: $$$[3, 3, 7, 6]$$$, $$$[3, 7, 7, 6]$$$ and $$$[7, 3, 7, 6]$$$.
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