Count Partitions Codechef Solution

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Count Partitions Codechef Solution

Count Partitions Codechef Solution

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Problem

An array B of length M consisting of only distinct elements is said to be good if the following condition holds:

  • Let i be the index of the maximum element of B.
  • Then, B[1,i] must be in ascending order, i.e, B_1 \lt B_2 \lt B_3 \lt \ldots \lt B_i.

For example, [1, 2, 3], [1, 4, 3, 2] and [1, 3, 2] are good arrays, while [2, 1, 3] and [3, 2, 4, 1] are not.

You are given a permutation P of length N. You have to partition P into some non-empty good subarrays. Note that every element of P should be contained in exactly one subarray.

Find the total number of valid partitions.

Since the answer can be quite large, please print it modulo 998244353.

Note: A permutation of length N is an arrangement of the integers \{1, 2, 3, \ldots, N\}.

Input Format

  • The first line of input contains a single integer T denoting the number of test cases. The description of T test cases follows.
  • Each test case consists of two lines of input.
    • The first line of each test case contains a single integer N, the length of P.
    • The second line contains N space-separated distinct integers P_1, P_2, P_3 , \ldots, P_N.

Output Format

For each test case, output on a new line the number of valid partitions modulo 998244353.

Constraints

  • 1 \leq T \leq 10^5
  • 1 \leq N \leq 10^6
  • 1 \leq P_i \leq N for each 1 \leq i \leq N.
  • All elements of P are distinct.
  • The sum of N over all test cases won’t exceed 10^6.

Sample 1:

Input

Output

2
4
2 1 4 3
5
1 2 3 4 5
6
16

Explanation:

Test case 1: The 6 valid partitions are as follows:

  • [2], [1], [4], [3]
  • [2], [1], [4, 3]
  • [2], [1, 4], [3]
  • [2], [1, 4, 3]
  • [2, 1], [4], [3]
  • [2, 1], [4, 3]
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SOLUTION

Count Partitions Codechef Solution

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