Score : $1000$ points

Problem Statement

Ringo has a string $S$.

He can perform the following $N$ kinds of operations any number of times in any order.

• Operation $i$: For each of the characters from the $L_i$-th through the $R_i$-th characters in $S$, replace it with its succeeding letter in the English alphabet. (That is, replace a with b, replace b with c and so on.) For z, we assume that its succeeding letter is a.

Ringo loves palindromes and wants to turn $S$ into a palindrome. Determine whether this is possible.

Constraints

• $1 \leq |S| \leq 10^5$
• $S$ consists of lowercase English letters.
• $1 \leq N \leq 10^5$
• $1 \leq L_i \leq R_i \leq |S|$

Input

Input is given from Standard Input in the following format:

$S$

$N$

$L_1$ $R_1$

$L_2$ $R_2$

$:$

$L_N$ $R_N$

Output

Print YES if it is possible to turn $S$ into a palindrome; print NO if it is impossible.

bixzja
2
2 3
3 6

YES

For example, if we perform Operation $1$, $2$ and $1$ in this order, $S$ changes as bixzja → bjyzja → bjzakb → bkaakb and becomes a palindrome.

abc
1
2 2

NO

cassert
4
1 2
3 4
1 1
2 2

YES