Problem D
Homework
Anthony has two multiple choice assignments to hand in today. The answer to each assignment is a string, where the $i^\textrm {th}$ letter represents the answer to the $i^\textrm {th}$ question.
But instead of handing in two strings, Anthony only hands in a single string. He claims he answered every question correctly but his little sister Cora merged his two strings into a single string. Moreover, Cora merged his string in such a way that the following conditions are satisfied:

For any two integers $0\leq i<j<s_1$ (where $s_1$ is the length of $s_1$), the index of $s_1[i]$ in $s$ is less than the index of $s_1[j]$ in $s$

For any two integers $0\leq i<j<s_2$, the index of $s_2[i]$ in $s$ is less than the index of $s_2[j]$ in $s$
Can you help Anthony’s teacher verify whether Anthony’s claim is possible?
Input
The first line contains a single string $s$. It is guaranteed that $2\leq s\leq 10\, 000$.
The next two lines contain strings $s_1$ and $s_2$ respectively. It is guaranteed that $1\leq s_1, s_2\leq 5\, 000$ and $s_1+s_2=s$.
All the strings consists of only lowercase English letters.
Output
If Anthony’s claim is possible, print “yes” (without quotes). Otherwise, print “no” (without quotes).
Sample Input 1  Sample Output 1 

aabcad aba acd 
yes 
Sample Input 2  Sample Output 2 

aabcad acb aad 
no 