You are given a permutation $P=(P _ 1,P _ 2,\ldots,P _ N)$ of $(1,2,\ldots,N)$.

Find the following value for all $i\ (1\leq i\leq N)$:

-   $D _ i=\displaystyle \min_{j\neq i} (\lvert P _ i-P_j  \rvert+ \lvert i-j \rvert  )$.

What is a permutation? A permutation of $(1,2,\ldots,N)$ is a sequence that is obtained by rearranging $(1,2,\ldots,N)$. In other words, a sequence $A$ of length $N$ is a permutation of $(1,2,\ldots,N)$ if and only if each $i\ (1\leq i\leq N)$ occurs in $A$ exactly once.

The input is given from Standard Input in the following format:

```
$N$
$P _ 1$ $P _ 2$ $\ldots$ $P _ N$
```

Print $D _ i\ (1\leq i\leq N)$ in ascending order of $i$, separated by spaces.

-   $2 \leq N \leq 2\times10^5$
-   $1 \leq P _ i \leq N\ (1\leq i\leq N)$
-   $i\neq j\implies P _ i\neq P _ j$
-   All values in the input are integers.

2 2 3 3 

For example, for i=1,

• if j=2, we have $∣P_i−P_j∣=1$ and ∣i−j∣=1;
• if j=3, we have $∣P_i−P_j∣=1$ and ∣i−j∣=2;
• if j=4, we have $∣P_i−P_j∣=2$ and ∣i−j∣=3.

Thus, the value is minimum when j=2, where $∣P_i−P_j∣+∣i−j∣=2$, so $D_1=2$.