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.*;
import java.util.StringTokenizer;

public class D {
    String filename = null;
    InputReader sc;

    static class Match {
        char winner = '1';
        int nCandidates = 1;

        Match m1, m2;
        Match next;

        void update() {
            if (winner == '?') {
                nCandidates = m1.nCandidates + m2.nCandidates;
            } else if (winner == '0') {
                nCandidates = m1.nCandidates;
            } else if (winner == '1') {
                nCandidates = m2.nCandidates;
            }
        }
    }

    void solve() throws IOException {
        int k = sc.nextInt();
        char[] s = sc.next(1 << 18).toCharArray();
        int nq = sc.nextInt();

        int n = 1;
        for (int i = 0; i < k; i++) {
            n *= 2;
        }

        Match[] matches = new Match[2 * n - 1];
        for (int i = 0; i < n; i++) {
            matches[i] = new Match();
        }

        int j = 0;
        for (int i = n; i < 2 * n - 1; i++) {
            matches[i] = new Match();
            matches[i].winner = s[i - n];

            matches[i].m1 = matches[j];
            matches[j].next = matches[i];
            j++;

            matches[i].m2 = matches[j];
            matches[j].next = matches[i];
            j++;

            assert(j <= i);
        }

        for (int i = n; i < 2 * n - 1; i++) {
            Match m = matches[i];
            m.update();
        }

        StringBuilder sb = new StringBuilder();
        for (int q = 0; q < nq; q++) {
            int p = sc.nextInt() - 1;
            char c = sc.next(2).charAt(0);

            matches[p + n].winner = c;
            Match m = matches[p + n];
            while (m != null) {
                m.update();
                m = m.next;
            }
            sb.append(matches[2 * n - 2].nCandidates + "\n");
        }
        
        System.out.println(sb);
    }

    public void run() throws IOException {
        if (filename == null) {
            sc = new InputReader(System.in);
        } else {
            sc = new InputReader(new FileInputStream(new File(filename)));
        }

        int nTests = 1;
        for (int test = 0; test < nTests; test++) {
            solve();
        }
    }

    public static void main(String[] args) {
        D sol = new D();
        try {
            sol.run();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    // source: https://www.geeksforgeeks.org/fast-io-in-java-in-competitive-programming/
    static class InputReader {
        final private int BUFFER_SIZE = 1 << 16;
        private final DataInputStream din;
        private final byte[] buffer;
        private int bufferPointer, bytesRead;

        public InputReader(InputStream is) {
            din = new DataInputStream(is);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public InputReader(String fileName) throws IOException {
            din = new DataInputStream(
                    new FileInputStream(fileName));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String nextLine(int maxSize) throws IOException {
            byte[] buf = new byte[maxSize]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') {
                    if (cnt != 0) {
                        break;
                    } else {
                        continue;
                    }
                }
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
        private byte skip() throws IOException { byte b; while((b = read()) != -1 && isSpaceChar(b)); return b; }

        public String next(int maxSize) throws IOException {
            byte b = skip();
            StringBuilder sb = new StringBuilder();
            while (!(isSpaceChar(b))) {
                sb.appendCodePoint(b);
                b = read();
            }
            return sb.toString();
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0,
                    BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            din.close();
        }

    }
}