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.

Sample Input 1

bixzja
2
2 3
3 6

Sample Output 1

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.

Sample Input 2

abc
1
2 2

Sample Output 2

NO

Sample Input 3

cassert
4
1 2
3 4
1 1
2 2

Sample Output 3

YES