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C - Airport Code

Time Limit: 2 sec / Memory Limit: 1024 MB

Score: $300$ points

Problem Statement

A string $T$ of length $3$ consisting of uppercase English letters is an airport code for a string $S$ of lowercase English letters if and only if $T$ can be derived from $S$ by one of the following methods:

  • Take a subsequence of length $3$ from $S$ (not necessarily contiguous) and convert it to uppercase letters to form $T$.
  • Take a subsequence of length $2$ from $S$ (not necessarily contiguous), convert it to uppercase letters, and append X to the end to form $T$.

Given strings $S$ and $T$, determine if $T$ is an airport code for $S$.

Constraints

  • $S$ is a string of lowercase English letters with a length between $3$ and $10^5$, inclusive.
  • $T$ is a string of uppercase English letters with a length of $3$.

Input

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

$S$

$T$

Output

Print Yes if $T$ is an airport code for $S$, and No otherwise.

Sample Input 1

narita
NRT

Sample Output 1

Yes

The subsequence nrt of narita, when converted to uppercase, forms the string NRT, which is an airport code for narita.

Sample Input 2

losangeles
LAX

Sample Output 2

Yes

The subsequence la of losangeles, when converted to uppercase and appended with X, forms the string LAX, which is an airport code for losangeles.

Sample Input 3

snuke
RNG

Sample Output 3

No