954. Number of Longest Increasing Subsequences

Given an integer array, return the number of longest strictly increasing subsequences. Two subsequences are different if they use different index sets. The input is a JSON array.

Input: A JSON array of integers.

Output: Integer — the count of longest increasing subsequences.

Examples

Input: [1,3,5,4,7]
Output: 2
Explanation: Two LIS of length 4.

Input: [2,2,2,2,2]
Output: 5
Explanation: Five LIS of length 1.

Input: [1,2,3]
Output: 1
Explanation: One LIS.

Constraints

• 1<=n<=2000
• -10^6<=value<=10^6

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