Spilled Ink

Didi defines $Z_i$ for a string $S$ of uppercase letters (A-Z) as the length of the longest common prefix of $S[1 \sim N]$ and the suffix $S[i \sim N]$ of $S$. Didi built the array $Z$ from these values using an algorithm found after long study. While dancing with joy, Didi spilled ink on part of the string $S$, so Didi cannot check whether the array $Z$ is correct.

The kind ryute wants to help the desperate Didi. Using the partially hidden string $S'$ and the array $Z$ that Didi wrote, ryute will restore the original string $S$. ryute will also check whether Didi's array $Z$ is correct. If at least one possible original string $S$ exists, the array $Z$ is considered correct. Otherwise, it is considered incorrect. Help ryute and Didi.

The first line contains the length $N$ of the string $S$ ($1 \le N \le 10^5$).

The second line contains the string $S'$. $S'$ consists of uppercase letters (A-Z) and #. A # means the letter at that position is hidden by ink. There are at most 20 # characters.

The third line contains the elements $Z_i$ ($0 \le Z_i \le N-i+1$) of the array $Z$ that Didi wrote, separated by spaces, in order.

If the array $Z$ that Didi wrote is incorrect, print THINKINGFACE. Otherwise, print YES on the first line and the original string $S$ on the second line. If several strings are possible for $S$, print any one of them.