A15061. Getting Zero

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 $0$ .

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.