An impassioned circulation of affection
Contest: Codeforces Round 418 (Div. 2)
Difficulty rating: 1600
Tags: brute force, dp, strings, two pointers

Nadeko's birthday is approaching! As she decorated the room for the party, a long garland of Dianthus-shaped paper pieces was placed on a prominent part of the wall. Brother Koyomi will like it!

Still unsatisfied with the garland, Nadeko decided to polish it again. The garland has n pieces numbered from 1 to n from left to right, and the i-th piece has a colour si, denoted by a lowercase English letter. Nadeko will repaint at most m of the pieces to give each of them an arbitrary new colour (still denoted by a lowercase English letter). After this work, she finds out all subsegments of the garland containing pieces of only colour c — Brother Koyomi's favourite one, and takes the length of the longest among them to be the Koyomity of the garland.

For instance, let's say the garland is represented by "kooomo", and Brother Koyomi's favourite colour is "o". Among all subsegments containing pieces of "o" only, "ooo" is the longest, with a length of 3. Thus the Koyomity of this garland equals 3.

But problem arises as Nadeko is unsure about Brother Koyomi's favourite colour, and has swaying ideas on the amount of work to do. She has q plans on this, each of which can be expressed as a pair of an integer mi and a lowercase letter ci, meanings of which are explained above. You are to find out the maximum Koyomity achievable after repainting the garland according to each plan.

Input format:
The first line of input contains a positive integer n (1 ≤ n ≤ 1 500) — the length of the garland.

The second line contains n lowercase English letters s1s2... sn as a string — the initial colours of paper pieces on the garland.

The third line contains a positive integer q (1 ≤ q ≤ 200 000) — the number of plans Nadeko has.

The next q lines describe one plan each: the i-th among them contains an integer mi (1 ≤ mi ≤ n) — the maximum amount of pieces to repaint, followed by a space, then by a lowercase English letter ci — Koyomi's possible favourite colour.

Output format:
Output q lines: for each work plan, output one line containing an integer — the largest Koyomity achievable after repainting the garland according to it.

Constraints:
Time limit: 2.0 s
Memory limit: 256.0 MB

Note:
In the first sample, there are three plans:

- In the first plan, at most 1 piece can be repainted. Repainting the "y" piece to become "o" results in "kooomi", whose Koyomity of 3 is the best achievable;
- In the second plan, at most 4 pieces can be repainted, and "oooooo" results in a Koyomity of 6;
- In the third plan, at most 4 pieces can be repainted, and "mmmmmi" and "kmmmmm" both result in a Koyomity of 5.

Example input:
6
koyomi
3
1 o
4 o
4 m

Example output:
3
6
5

Example input:
15
yamatonadeshiko
10
1 a
2 a
3 a
4 a
5 a
1 b
2 b
3 b
4 b
5 b

Example output:
3
4
5
7
8
1
2
3
4
5

Editorial:
The first thing to notice is that we are only changing other colours to Koyomi's favourite one. Furthermore, we won't create disconnected segments of that colour, for that's no better than painting just around the longest among them.
This leads us to a straightforward approach: when faced with a query (m, c), we check each segment [l, r] and determine whether it's possible to fill this segment with letter c, within at most m replacements. This can be done by finding the number of times c occurs in that segment (denote it by tc), and checking whether (r - l + 1) - t ≤ m. But this O(n2·q) solution would be too slow.
Since the number of different queries is 26n, we can calculate all answers beforehand. For each letter c and a segment [l, r], we'll be able to fill the whole segment with c within (r - l + 1) - tc moves. Use this information to update the answers, and employing a "prefix max" method gives us a time complexity of O(n2·|Σ| + q), where |Σ| equals 26. Refer to the code for a possible implementation.
Bonus. Find out the O(n2  +  n·|Σ|  +  q) solutions and the O(nq) solutions (some of them may get TLE — remember to check against maximum data next time!).