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

Solution in Julia (1.4.0) (judge verdict: Time Limit Exceeded)

readint()=parse.(Int,readline())
N=readint()
S=readline()
popcount(n)=sum(digits(n,base=2))
function f(n)
    s=0
    while n!=0
        n%=popcount(n)
        s+=1
    end
    s
end
function bitRev(X,N,i)
    if (X >> (N-i) & 1)==1
        X-=2^(N-i)
    else
        X+=2^(N-i)
    end
    X
end
#X=parse(Int,S,base=2)
Ss=split(S,"")
function bit2Int(N,Ss)
  X=0
	for i in 1:N
   		Ss[i]=="1" && (X+=big(2)^(N-i))
	end
  X
end
X=bit2Int(N,Ss)
for i in 1:N
    println(f(bitRev(X,N,i)))
end