Description

Given an integer n, return an array ans of length n+1 where ans[i] is the number of 1's in the binary representation of i.

Examples

Input:n = 5
Output:[0,1,1,2,1,2]
Explanation:

0=0, 1=1, 2=10, 3=11, 4=100, 5=101

Input:n = 0
Output:[0]
Explanation:

For n=0, only the number 0 is counted. The binary representation of 0 is '0', which contains zero 1's.

Input:n = 7
Output:[0,1,1,2,1,2,2,3]
Explanation:

For n=7: 0=0 (0 ones), 1=1 (1 one), 2=10 (1 one), 3=11 (2 ones), 4=100 (1 one), 5=101 (2 ones), 6=110 (2 ones), 7=111 (3 ones)

Constraints

  • 0 ≤ n ≤ 10⁵

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