An impassioned circulation of affection

给你一个由小写字母构成的字符串 $s$ 和 $q$ 次询问，每个询问给出数字 $m$ 和小写字母 $c$。你可以任意地修改字符串中的 $m$ 个字符，求最多能够使字符串中含有多少个连续相同的字母 $c$。 每个询问各自独立。保证 $1\leqslant\left\vert s\right\vert\leqslant 1500,1\leqslant q\leqslant2\times10^5,1\leqslant m_i\leqslant n$。

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 $ s_{i} $ , 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 $ m_{i} $ and a lowercase letter $ c_{i} $ , meanings of which are explained above. You are to find out the maximum Koyomity achievable after repainting the garland according to each plan.

The first line of input contains a positive integer $ n $ ( $ 1<=n<=1500 $ ) — the length of the garland. The second line contains $ n $ lowercase English letters $ s_{1}s_{2}...\ s_{n} $ as a string — the initial colours of paper pieces on the garland. The third line contains a positive integer $ q $ ( $ 1<=q<=200000 $ ) — the number of plans Nadeko has. The next $ q $ lines describe one plan each: the $ i $ -th among them contains an integer $ m_{i} $ ( $ 1<=m_{i}<=n $ ) — the maximum amount of pieces to repaint, followed by a space, then by a lowercase English letter $ c_{i} $ — Koyomi's possible favourite colour.

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

6
koyomi
3
1 o
4 o
4 m

3
6
5

15
yamatonadeshiko
10
1 a
2 a
3 a
4 a
5 a
1 b
2 b
3 b
4 b
5 b

3
4
5
7
8
1
2
3
4
5

10
aaaaaaaaaa
2
10 b
10 z

10
10

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 $ .