题目描述

Given a sequence of 12 numbers consisting of 0 and the first 11 natural numbers. Suppose number 0 is in the i-th position of the sequence (positions are numbered from 0 to 11). You can swap it with the number in the j-th position if the following conditions hold:

• | i – j | = d $_{k}$ , where k=1..3 and (d $_{1}$ ,d $_{2}$ ,d $_{3}$ ,d $_{4}$ )=(1;3;6;12)
• floor(i/d $_{k+1}$ )=floor(j/d $_{k+1}$ )

Your task is to find the minimum number of exchange operations required to sort the sequence in increasing order.

输入格式

输入数据由多组数据组成。

每一组数据由一行12个数构成P_{i}表示i号位置上的箱子编号。

输出格式

一个数，最少的交换次数。

2
1 10 2 3 0 5 7 4 8 6 9 11
6 4 1 0 3 5 9 7 2 10 11 8

8
9

提示

数据约定： 数据组数不超过100。 对于每一组数据，对应的答案不会“非常大”