Score : $1300$ points

Problem Statement

You are developing a robot that processes strings. When the robot is given a string $t$ consisting of lowercase English letters, it processes the string by following the procedure below:

1. Let $i$ be the smallest index such that $t_i = t_{i + 1}$. If such an index does not exist, terminate the procedure.
2. If $t_i$ is z, remove $t_i$ and $t_{i + 1}$ from $t$. Otherwise, let $c$ be the next letter of $t_i$ in the English alphabet, and replace $t_i$ and $t_{i + 1}$ together with $c$, reducing the length of $t$ by $1$.
3. Go back to step 1.

For example, when the robot is given the string axxxxza, it will be processed as follows: axxxxza → ayxxza → ayyza → azza → aa → b.

You are given a string $s$ consisting of lowercase English letters. Answer $Q$ queries. The $i$-th query is as follows:

• Assume that the robot is given a substring of $s$ that runs from the $l_i$-th character and up to the $r_i$-th character (inclusive). Will the string be empty after processing?

Constraints

• $1 \leq |s| \leq 5 \times 10^5$
• $s$ consists of lowercase English letters.
• $1 \leq Q \leq 10^5$
• $1 \leq l_i \leq r_i \leq |s|$

Input

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

$s$

$Q$

$l_1$ $r_1$

$l_2$ $r_2$

$:$

$l_Q$ $r_Q$

Output

Print $Q$ lines. The $i$-th line should contain the answer to the $i$-th query: Yes or No.

axxxxza
2
1 7
2 6

No
Yes

• Regarding the first query, the string will be processed as follows: axxxxza → ayxxza → ayyza → azza → aa → b.
• Regarding the second query, the string will be processed as follows: xxxxz → yxxz → yyz → zz → ``.

aabcdefghijklmnopqrstuvwxyz
1
1 27

Yes

yzyyyzyzyyyz
8
1 6
7 12
1 12
6 11
1 1
1 3
4 9
3 8

Yes
Yes
Yes
Yes
No
No
No
No