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

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

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

Examples

Input

6
koyomi
3
1 o
4 o
4 m


Output

3
6
5


Input

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


Output

3
4
5
7
8
1
2
3
4
5


Input

10
aaaaaaaaaa
2
10 b
10 z


Output

10
10

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. 
20
aaaaaaaaaaaaaaaaaaaa
1
11 a
 4
cbcc
12
4 b
4 c
1 b
2 a
3 b
2 c
4 a
1 a
2 b
3 a
1 c
3 c
 100
dddddccccdddddaaaaabbbbbbbbbbbbbaaacdcabbacccacccccbdbbadddbbddddbdaaccacdddbbbaddddbbbbdcbbbdddddda
50
54 b
48 d
45 b
52 c
52 a
48 a
54 b
45 a
47 d
50 d
53 a
34 a
51 b
48 d
47 d
47 a
48 d
53 b
52 d
54 d
46 a
38 a
52 b
49 a
49 b
46 c
54 a
45 b
35 c
55 c
51 c
46 d
54 d
50 a
33 c
46 a
50 b
50 a
54 a
32 b
55 b
49 c
53 d
49 a
46 b
48 c
47 b
47 b
47 a
46 b
 5
aaaaa
1
1 b
 4
ddbb
16
3 c
3 b
1 a
1 b
4 d
4 a
3 d
2 a
2 d
4 c
3 a
2 c
4 b
1 c
2 b
1 d
 4
abcc
24
1 c
4 d
3 c
1 d
1 c
1 b
3 b
2 c
3 d
3 d
4 c
2 a
4 d
1 a
1 b
4 a
4 d
3 b
4 b
3 c
3 a
2 d
1 a
2 b
 1
c
4
1 x
1 a
1 e
1 t
 40
cbbcbcccccacccccbbacbaabccbbabbaaaaacccc
10
40 a
28 c
25 c
21 a
18 c
27 a
9 c
37 c
15 a
18 b
 200
ddeecdbbbeeeeebbbbbaaaaaaaaaaaaaaaaaaaaaaabbcaacccbeeeeddddddddddddccccccdffeeeeecccccbbbbaaaaedfffffaadeeeeeeeedddddaaaaaaaaaaaaaabbbbbcaadddeefffbbbbcccccccccccbbbbbbeeeeeeeffffffdffffffffffffaaaaab
10
43 f
118 d
165 f
72 f
48 f
2 a
61 e
94 d
109 f
16 a

20
 4
4
2
2
4
4
4
1
3
3
4
4
 85
72
76
69
68
63
85
60
71
74
69
46
82
72
71
62
72
84
76
78
61
50
83
64
80
60
70
76
49
72
68
70
78
66
47
61
81
66
70
53
86
63
77
64
77
62
78
78
62
77
 1
 3
4
1
3
4
4
4
2
4
4
3
2
4
1
4
3
 3
4
4
1
3
2
4
4
3
3
4
3
4
2
2
4
4
4
4
4
4
2
2
3
 1
1
1
1
 40
40
40
31
35
37
23
40
24
27
 64
144
193
98
69
25
79
117
137
41

import java.util.*;
import java.io.*;

public class Garland{
	public static void main(String arsg[]) throws Exception{
		FastScanner in  = new FastScanner(System.in);
		int n = in.nextInt();
		System.out.println("Read n "+n);
		String str = in.next();
		System.out.println("what is "+str);
		char [] garland = str.toCharArray();
		int q = in.nextInt();
		System.out.println("Read q "+q);
	     StringBuilder build = new StringBuilder();
		int [][] minValues = prepareMinValues(garland);
		for(int t = 0;t<q;t++){
		  	int m = in.nextInt();
			char c = in.next().charAt(0);
			System.out.println(m+" + "+c);
			int result = getMaxSlice(minValues, m, c);
			build.append(result).append("\n");
		}
		in.close();
		System.out.println(build.toString());
     }
	private static final int  ALPH_SIZE = 26;
	private static int [][] prepareMinValues(char [] garland){
			int [][] res =  new int[ALPH_SIZE][garland.length+1];
			for(char ch = 'a';ch<='z';ch++){
				int i = ch-'a';
				for(int l = 1;l<=garland.length;l++){
					int min = l;
					int gaps = 0;
					for(int j = 0;j<garland.length;j++){
						if(garland[j] != ch) gaps++;						 
						if(j>=l){
							if(garland[j-l] != ch) gaps--;
							min = Math.min(min, gaps);
						}
					}
					//System.out.println("min for "+ch+" is "+gaps);
					min = Math.min(min, gaps);
					res[i][l] = min;
				}
			}
			return res;
	}

	private static int getMaxSlice(int [][] minValues, int m, char c){
		int [] vals = minValues[c-'a'];
		int l = m, r = vals.length-1;
		int ans = m;
		while(l<=r){
			int v = (l+r)/2;
			if(vals[v] <= m){
				ans = Math.max(ans, v);
				l = v+1;
			} else {
				r = v-1;
			}
		}
		return ans;
	}

}

class FastScanner {

    static final int DEFAULT_BUFF = 1024, EOF = -1, INT_MIN = 48, INT_MAX = 57, NOT_SET = -1, POS = 1, DOT=46, SPACE=32, NL = 10, CR = 13;
    static final byte NEG = 45;
    /**
     * Stores digits for corresponding byte values
     */
    static final int[] digits = new int[58];

    /**
     * Assigning digits for corresponding byte values
     */
    static {
        int value = 0;
        for (int i = 48; i < 58; i++) {
            digits[i] = value++;
        }
    }

    InputStream stream;
    /**
     * Current buffer of bytes in memory
     */
    byte[] buff;
    /**
     * Pointer that points to the byte position in bytes buffer array
     */
    int buffPtr;

    /**
     * Constructor of FastScanner with default bytes buffer size
     *
     * @param stream - input stream to scan
     */
    public FastScanner(InputStream stream) {
        this.stream = stream;
        this.buff = new byte[DEFAULT_BUFF];
        this.buffPtr = NOT_SET;
    }

    /**
     * Constructor of FastScanner with custom bytes buffer size
     *
     * @param stream - input stream to scan
     * @param bufferSize - custom buffer size to read bytes into
     */
    public FastScanner(InputStream stream, int bufferSize) {
        this.stream = stream;
        this.buff = new byte[bufferSize];
        this.buffPtr = NOT_SET;
    }

    /**
     * Method for obtaining next available 32 bit integer from the input. Not
     * that it just skips all the non numeric characters around numeric slice
     * and returns the numeric slice.
     *
     * @return - 32 bit integer value if one exist in input.
     * @throws IOException if no more digits are found
     */
    public int nextInt() throws IOException {
        int val = 0;
        int sign = readNonNumerics();
        while (isDigit(buff[buffPtr]) && buff[buffPtr] != EOF) {
            val = (val << 3) + (val << 1) + digits[buff[buffPtr]];
            buffPtr++;
            if (buffPtr == buff.length) {
                updateBuff();
            }
        }
        return val * sign;
    }
     /**
     * Method for obtaining next available 64 bit integer from the input. Not
     * that it just skips all the non numeric characters around numeric slice
     * and returns the numeric slice.
     *
     * @return - 64 bit integer value if one exist in input.
     * @throws IOException if no more digits are found
     */
    public long nextLong() throws IOException {
        long val = 0L;
        int sign = readNonNumerics();
        while (isDigit(buff[buffPtr]) && buff[buffPtr] != EOF) {
            val = (val << 3) + (val << 1) + digits[buff[buffPtr]];
            buffPtr++;
            if (buffPtr == buff.length) {
                updateBuff();
            }
        }
        return val * sign;
    }
    /**
     * Reads next string slice 
     * @return String the next available string without space characters
     * @throws IOException if some exception occurs while input output
     */
    public String next() throws IOException{
        readAllSpaces();
        StringBuilder res = new StringBuilder();
        while(buff[buffPtr] != SPACE && buff[buffPtr] != NL && buff[buffPtr] != CR){
            res.append((char)buff[buffPtr]);
            buffPtr++;
            if(buffPtr >= buff.length){
                updateBuff();
            }
        }
        return res.toString();
    }
    
    /**
     * Reads all non numeric symbols and assigns the buffer's pointer to the
     * first available numeric character byte
     *
     * @return integer sign denoting the sign of the integer to be red next
     * @throws IOException if no more numeric character is found
     */
    private int readNonNumerics() throws IOException {
        if (buffPtr == NOT_SET || buffPtr == buff.length) {
            updateBuff();
        }
        if (buff[buffPtr] == EOF) {
            throw new IOException("End of stream reached");
        }
        int signByte = NOT_SET;
        while (!isDigit(buff[buffPtr])) {
            signByte = buff[buffPtr];
            buffPtr++;
            if (buffPtr >= buff.length) {
                updateBuff();
            }
            if (buff[buffPtr] == EOF) {
                throw new IOException("End of stream reached");
            }
        }
        if (signByte == NEG) {
            return -POS;
        }
        return POS;
    }

    private void readAllSpaces() throws IOException{
        if (buffPtr == NOT_SET || buffPtr == buff.length) {
            updateBuff();
        }
	   System.out.println("the char is "+buff[buffPtr]);
        if (buff[buffPtr] == EOF) {
            throw new IOException("End of stream reached");
        }
        while(buff[buffPtr] == SPACE || buff[buffPtr] == NL || buff[buffPtr] == CR){
            buffPtr++;
            if(buffPtr>=buff.length){
                updateBuff();
            }
            if(buff[buffPtr] == EOF){
                throw new IOException("End of stream reached");
            }
        }
	   System.out.println("2) the char is "+buff[buffPtr]);
    }
    
    /**
     * Closes the input stream passed as parameter to a constructor. We
     * recommend to avoid calling this method explicitly if not necessary!
     *
     * @throws IOException if some exception occurs while closing the stream
     */
    public void close() throws IOException {
        stream.close();
    }

    /**
     * Checks whether byte is for numeric character
     *
     * @param b - byte number of character
     * @return true if the input byte number is for numeric character
     */
    private boolean isDigit(int b) {
        return b >= INT_MIN && b <= INT_MAX;
    }

    /**
     * Loads next buffer of bytes and resets the buffer pointer
     *
     * @throws IOException if some exception occurs while reading bytes into the
     * buffer array.
     */
    private void updateBuff() throws IOException {
        buffPtr = 0;
        stream.read(buff);
    }
}

