Problem:


Score : 400 points

Problem Statement

Let \mathrm{popcount}(n) be the number of 1s in the binary representation of n.
For example, \mathrm{popcount}(3) = 2, \mathrm{popcount}(7) = 3, and \mathrm{popcount}(0) = 0.

Let f(n) be the number of times the following operation will be done when we repeat it until n becomes 0: "replace n with the remainder when n is divided by \mathrm{popcount}(n)." (It can be proved that, under the constraints of this problem, n always becomes 0 after a finite number of operations.)

For example, when n=7, it becomes 0 after two operations, as follows:

\mathrm{popcount}(7)=3, so we divide 7 by 3 and replace it with the remainder, 1.

\mathrm{popcount}(1)=1, so we divide 1 by 1 and replace it with the remainder, 0.

You are given an integer X with N digits in binary.
For each integer i such that 1 \leq i \leq N, let X_i be what X becomes when the i-th bit from the top is inverted.
Find f(X_1), f(X_2), \ldots, f(X_N).

Constraints

1 \leq N \leq 2 \times 10^5

X is an integer with N digits in binary, possibly with leading zeros.

Input

Input is given from Standard Input in the following format:

N
X

Output

Print N lines. The i-th line should contain the value f(X_i).

Sample Input 1

3
011

Sample Output 1

2
1
1

X_1 = 7, which will change as follows: 7 \rightarrow 1 \rightarrow 0. Thus, f(7) = 2.

X_2 = 1, which will change as follows: 1 \rightarrow 0. Thus, f(1) = 1.

X_3 = 2, which will change as follows: 2 \rightarrow 0. Thus, f(2) = 1.

Sample Input 2

23
00110111001011011001110

Sample Output 2

2
1
2
2
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
3



Sample input:
3
011


Sample output:
2
1
1

Submission status: Runtime Error

Solution code:
# -*- coding: utf-8 -*-
import sys
import math
from bisect import bisect_left
from bisect import bisect_right
from collections import defaultdict
from heapq import heappop, heappush
import itertools
import random
from collections import deque
from decimal import *
import queue

input = sys.stdin.readline

def inputInt(): return int(input())
def inputMap(): return map(int, input().split())
def inputList(): return list(map(int, input().split()))
def inputStr(): return input()[:-1]

inf = float('inf')
mod = 1000000007

#-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-
#-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-

def main():
	N = inputInt()
	X = inputStr()
	X_lin = list(X)

	ans = []
	mem = {}
	for i in range(N):
		tmpX = X_lin
		if X[i] == "1":
			tmpX = X[:i] + "0" + X[i+1:]
		else:
			tmpX = X[:i] + "1" + X[i+1:]

		oct = int(tmpX, 2)

		ans_tmp = 0
		if oct in mem:
			ans_tmp = mem[oct]

		else:
			while True:
				if oct == 0:
					break
				tmp = bitsoncount(oct)
				oct = oct % tmp
				ans_tmp += 1
				if oct == 0:
					break
				if oct in mem:
					ans_tmp += mem[oct]
					break

		if oct in mem:
			pass
		else:
			mem[oct] = ans_tmp

		ans.append(ans_tmp)

	for i in ans:
		print(i)

def bitsoncount(i):
    assert 0 <= i < 0x100000000
    i = i - ((i >> 1) & 0x55555555)
    i = (i & 0x33333333) + ((i >> 2) & 0x33333333)
    return (((i + (i >> 4) & 0xF0F0F0F) * 0x1010101) & 0xffffffff) >> 24

#-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-
#-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-
if __name__ == "__main__":
	main()

Submission status: Runtime Error

Solution code:
from functools import lru_cache


@lru_cache(maxsize=None)
def popcount(x):
    x = x - ((x >> 1) & 0x5555555555555555)
    x = (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333)
    x = (x + (x >> 4)) & 0x0f0f0f0f0f0f0f0f
    x = x + (x >> 8)
    x = x + (x >> 16)
    x = x + (x >> 32)
    x = x + (x >> 64)
    return x & 0x0000007f


@lru_cache(maxsize=None)
def rec(n):
    if n == 0:
        return 0
    else:
        return rec(n % popcount(n)) + 1


n = int(input())
arr = input()

li = []

for i in range(n):
    tmp = arr[:i] + str(1 ^ int(arr[i])) + arr[i + 1:]
    li.append(int(tmp, 2))

for x in li:
    print(rec(x))