Getting Zero
Description
Suppose you have an integer $v$. In one operation, you can:
- either set $v = (v + 1) \bmod 32768$
- or set $v = (2 \cdot v) \bmod 32768$.
You are given $n$ integers $a_1, a_2, \dots, a_n$. What is the minimum number of operations you need to make each $a_i$ equal to $0$?
The first line contains the single integer $n$ ($1 \le n \le 32768$) — the number of integers.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i < 32768$).
Print $n$ integers. The $i$-th integer should be equal to the minimum number of operations required to make $a_i$ equal to $0$.
Input
The first line contains the single integer $n$ ($1 \le n \le 32768$) — the number of integers.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i < 32768$).
Output
Print $n$ integers. The $i$-th integer should be equal to the minimum number of operations required to make $a_i$ equal to $0$.
Samples
4
19 32764 10240 49
14 4 4 15
Note
Let's consider each $a_i$:
- $a_1 = 19$. You can, firstly, increase it by one to get $20$ and then multiply it by two $13$ times. You'll get $0$ in $1 + 13 = 14$ steps.
- $a_2 = 32764$. You can increase it by one $4$ times: $32764 \rightarrow 32765 \rightarrow 32766 \rightarrow 32767 \rightarrow 0$.
- $a_3 = 10240$. You can multiply it by two $4$ times: $10240 \rightarrow 20480 \rightarrow 8192 \rightarrow 16384 \rightarrow 0$.
- $a_4 = 49$. You can multiply it by two $15$ times.