Problem: 2^k teams participate in a playoff tournament. The tournament consists of 2^k - 1 games. They are held as follows: first of all, the teams are split into pairs: team 1 plays against team 2, team 3 plays against team 4 (exactly in this order), and so on (so, 2^{k-1} games are played in that phase). When a team loses a game, it is eliminated, and each game results in elimination of one team (there are no ties). After that, only 2^{k-1} teams remain. If only one team remains, it is declared the champion; otherwise, 2^{k-2} games are played: in the first one of them, the winner of the game "1 vs 2" plays against the winner of the game "3 vs 4", then the winner of the game "5 vs 6" plays against the winner of the game "7 vs 8", and so on. This process repeats until only one team remains.

For example, this picture describes the chronological order of games with k = 3:

<image>

Let the string s consisting of 2^k - 1 characters describe the results of the games in chronological order as follows:

  * if s_i is 0, then the team with lower index wins the i-th game; 
  * if s_i is 1, then the team with greater index wins the i-th game; 
  * if s_i is ?, then the result of the i-th game is unknown (any team could win this game). 



Let f(s) be the number of possible winners of the tournament described by the string s. A team i is a possible winner of the tournament if it is possible to replace every ? with either 1 or 0 in such a way that team i is the champion.

You are given the initial state of the string s. You have to process q queries of the following form: 

  * p c — replace s_p with character c, and print f(s) as the result of the query. 

Input

The first line contains one integer k (1 ≤ k ≤ 18).

The second line contains a string consisting of 2^k - 1 characters — the initial state of the string s. Each character is either ?, 0, or 1.

The third line contains one integer q (1 ≤ q ≤ 2 ⋅ 10^5) — the number of queries.

Then q lines follow, the i-th line contains an integer p and a character c (1 ≤ p ≤ 2^k - 1; c is either ?, 0, or 1), describing the i-th query.

Output

For each query, print one integer — f(s).

Example

Input


3
0110?11
6
5 1
6 ?
7 ?
1 ?
5 ?
1 1


Output


1
2
3
3
5
4

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int k = in.nextInt();
            long possibleVictors = 0;
            String s = in.readLine();
            // what we care is what we elinminate each step
            // elinmination works like this

            // lets setup our tree
            // what do we do once our tree is setup?
            // we can propogate forward and backwards
            // moving forward on our tree
            // tree is k levels deep

            // lets fill out status first

            // lets setup our nodes
            // by level
            int sIdx = 0;
            TreeNode[] nodes = new TreeNode[s.length()];

            for (int nk = k - 1; nk >= 0; nk--) {
                for (int z = 0; z < Math.pow(2, nk); z++) {
                    TreeNode n = new TreeNode();
                    nodes[sIdx] = n;
                    int prevIdxa = getPrevIdx(sIdx, s.length());
                    int prevIdxb = prevIdxa - 1;
                    if (prevIdxa >= 0) {
                        TreeNode prevNodea = nodes[prevIdxa];
                        TreeNode prevNodeb = nodes[prevIdxb];
                        prevNodea.nextGame = n;
                        prevNodeb.nextGame = n;
                        n.prevGame1 = prevNodea;
                        n.prevGame2 = prevNodeb;
                        n.prevGame1.nextGame = n;
                        n.prevGame2.nextGame = n;
                    }

                    n.status = s.charAt(sIdx);
                    n.recalculate();
                    sIdx++;
                }
            }

            int queries = in.nextInt();
            for (; queries > 0; queries--) {
                int idx = in.nextInt() - 1;
                char status = in.nextString().charAt(0);
                TreeNode n = nodes[idx];
                n.status = status;
                n.recalculate();
                out.println(nodes[s.length() - 1].possibleVictors);
            }

        }

        private int getPrevIdx(int n, int l) {
            int dist = l - n;
            int idx = dist * 2;
            return l - idx;
        }

        private class TreeNode {
            long possibleVictors;
            TreeNode nextGame;
            TreeNode prevGame1;
            TreeNode prevGame2;
            char status;

            private void recalculate() {
                // something changed, what do we do
                // we tell our parent to recalculate
                if (status == '0') {
                    if (prevGame2 != null) {
                        possibleVictors = prevGame2.possibleVictors;
                    } else {
                        possibleVictors = 1;
                    }
                } else if (status == '1') {
                    if (prevGame1 != null) {
                        possibleVictors = prevGame1.possibleVictors;
                    } else {
                        possibleVictors = 1;
                    }
                } else {
                    if (prevGame2 != null) {

                        possibleVictors = prevGame1.possibleVictors + prevGame2.possibleVictors;
                    } else {
                        possibleVictors = 2;
                    }
                }

                if (nextGame != null) {
                    nextGame.recalculate();
                }


            }

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String nextString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                if (Character.isValidCodePoint(c)) {
                    res.appendCodePoint(c);
                }
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private String readLine0() {
            StringBuilder buf = new StringBuilder();
            int c = read();
            while (c != '\n' && c != -1) {
                if (c != '\r') {
                    buf.appendCodePoint(c);
                }
                c = read();
            }
            return buf.toString();
        }

        public String readLine() {
            String s = readLine0();
            while (s.trim().length() == 0) {
                s = readLine0();
            }
            return s;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}