You are given an integer $x$ represented as a product of $n$ its *prime* divisors $p_1\cdot p_2\cdot p_3\cdots p_n$. Let $S$ be the set of all positive integer divisors of $x$ (including $1$ and $x$ itself). We call a set of integers $D$ *good* if (and only if) there is no pair $a\in D,b\in D$ such that $a\neq b$ and $a$ divides $b$. Find a *good* subset of $S$ with maximum possible size. Since the answer can be large, print the size of the subset modulo $998244353$.

The first line contains the single integer $n\ (1\le n\le 2\cdot 10^5)$ — the number of prime divisors in representation of $x$. The second line contains $n$ integers $p_1,p_2,p_3,\cdots,p_n\ (2\le p_i\le 3\cdot 10^6)$ — the prime factorization of $x$.

Print the maximum possible size of a *good* subset modulo $998244353$.

In the first sample, $x=2999999\cdot 43\cdot 2999957$ and one of the maximum *good* subsets is $\{43,2999957,2999999\}$. In the second sample, $x=2\cdot 3\cdot 2\cdot 3\cdot 2\cdot 2=144$ and one of the maximum *good* subsets is $\{9,12,16\}$.

Codeforces Educational [CF1257G]