Uolevi has bought a new computer. He immediately installed his favourite operating system "PeeloOS" on it. Unfortunately:

• Due to an integration problem with his hardware, he can only create one folder
• Due to a bug in the OS, he cannot create a folder with the string F as it's name's subsequence.

Uolevi really wanted to create two empty folders with names A and B, but since he cannot do that, he wants the next best thing: to create a folder that is just A and B fused together! Formally, Uolevi wants to find a string S such that

• A is a subsequence of S
• B is a subsequence of S
• F is not a subsequence of S

can you tell him whether any such S exists?

A subsequence of a string is any string that can be created by removing some letters from the original string, without changing the order of the remaining letters. For example, ab is aab's subsequence, but ba or aaa are not.

Input

The first line contains three integers: \left|A\right|, \left|B\right|, \left|F\right|.
The second of input contains the string A.
The third line of input contains the string B.
The fourth line of input contains the string F.

Output

Output YES if any such string S exists and NO otherwise.

Constraints

• 1 \leq \left|A\right|, \left|B\right|, \left|F\right| \leq 25000
• all characters in all strings are lowercase English letters from 'a' to 'z'

Example

Input:

6 6 6
abbacc
bacbac
bbaacc

Output:

YES

Explanation:
one such string is babbcbacc

Input:

3 3 2
aab
aba
ab

Output:

NO