output_description: Print the answer.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      \(N\)
      \(a_1\) \(a_2\) \(\ldots\) \(a_N\)
attempt: print("3")
  
problem_description: Statement
  
  Niwango-kun has \\(N\\) chickens as his pets. The chickens are identified by
  numbers \\(1\\) to \\(N\\), and the size of the \\(i\\)-th chicken is a
  positive integer \\(a_i\\).
  
  \\(N\\) chickens decided to take each other's hand (wing) and form some
  cycles. The way to make cycles is represented by a permutation \\(p\\) of
  \\(1, \ldots , N\\). Chicken \\(i\\) takes chicken \\(p_i\\)'s left hand by
  its right hand. Chickens may take their own hand.
  
  Let us define the _cycle_ containing chicken \\(i\\) as the set consisting of
  chickens \\(p_i, p_{p_i}, \ldots, p_{\ddots_i} = i\\). It can be proven that
  after each chicken takes some chicken's hand, the \\(N\\) chickens can be
  decomposed into cycles.
  
  The _beauty_ \\(f(p)\\) of a way of forming cycles is defined as the product
  of the size of the smallest chicken in each cycle. Let \\(b_i \ (1 \leq i \leq
  N)\\) be the sum of \\(f(p)\\) among all possible permutations \\(p\\) for
  which \\(i\\) cycles are formed in the procedure above.
  
  Find the greatest common divisor of \\(b_1, b_2, \ldots, b_N\\) and print it
  \\({\rm mod} \ 998244353\\).
samples: [{"input": "2\n    4 3", "output": "3\n    \n\nIn this case, \\\\(N = 2, a = [ 4, 3 ]\\\\).\n\nFor the permutation \\\\(p = [ 1, 2 ]\\\\), a cycle of an only chicken \\\\(1\\\\) and\na cycle of an only chicken \\\\(2\\\\) are made, thus \\\\(f([1, 2]) = a_1 \\times\na_2 = 12\\\\).\n\nFor the permutation \\\\(p = [ 2, 1 ]\\\\), a cycle of two chickens \\\\(1\\\\) and\n\\\\(2\\\\) is made, and the size of the smallest chicken is \\\\(a_2 = 3\\\\), thus\n\\\\(f([2, 1]) = a_2 = 3\\\\).\n\nNow we know \\\\(b_1 = f([2, 1]) = 3, b_2 = f([1, 2]) = 12\\\\), and the greatest\ncommon divisor of \\\\(b_1\\\\) and \\\\(b_2\\\\) is \\\\(3\\\\).\n\n* * *"}, {"input": "4\n    2 5 2 5", "output": "2\n    \n\nThere are always \\\\(N!\\\\) permutations because chickens of the same size can\nbe distinguished from each other.\n\nThe following picture illustrates the cycles formed and their beauties when\n\\\\(p = (2, 1, 4, 3)\\\\) and \\\\(p = (3, 4, 1, 2)\\\\), respectively.\n\n![bdd8ce0a7db3b4f920b04551c60aa207.png](https://img.atcoder.jp/dwacon5th-\nprelims/bdd8ce0a7db3b4f920b04551c60aa207.png)"}]