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).

Examples

Input

3
011

Output

2
1
1

Input

23
00110111001011011001110

Output

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

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