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.*;

public class PlayOffTournament implements Runnable {

   Node[] arr;
   String s;

   void solve() {
      int n = ri();
      s = rs();
      int len = s.length();
      arr = new Node[len];

      constructGraph();
      int t = ri();
      while (t-- > 0) {
         int index = ri();
         arr[index - 1].c = rc();
         update(arr[index - 1]);
         println(arr[arr.length - 1].count);
      }
   }

   void update(Node node) {
      if (node.left == null & node.right == null) {
         node.count = (node.c == '?') ? 2 : 1;
      } else {
         if (node.c == '?') {
            node.count = node.left.count + node.right.count;
         } else if (node.c == '1') {
            node.count = node.right.count;
         } else {
            node.count = node.left.count;
         }
      }
      if (node.parent != null)
         update(node.parent);
   }

   void constructGraph() {
      int currIndex = s.length() - 1;
      ArrayDeque<Node> queue = new ArrayDeque<>();
      arr[currIndex] = new Node();
      queue.add(arr[currIndex]);

      int count = 0;
      while (!queue.isEmpty()) {
         int len = queue.size();
         currIndex -= (count == 0) ? 0 : (1 << count);
         for (int i = 0; i < len; i++) {
            Node curr = queue.poll();
            curr.c = s.charAt(currIndex + i);
            arr[currIndex + i] = curr;
            if (currIndex != 0) {
               curr.left = new Node();
               curr.left.parent = curr;
               curr.right = new Node();
               curr.right.parent = curr;
               queue.add(curr.left);
               queue.add(curr.right);
            }
         }
         count++;
      }

      dfsConstruct(arr[s.length() - 1]);
   }

   void dfsConstruct(Node node) {
      if (node.left == null && node.right == null) {
         node.count = (node.c == '?') ? 2 : 1;
      } else {
         dfsConstruct(node.left);
         dfsConstruct(node.right);

         if (node.c == '?') {
            node.count = node.left.count + node.right.count;
         } else if (node.c == '1') {
            node.count = node.right.count;
         } else {
            node.count = node.left.count;
         }
      }
   }

   class Node {
      char c;
      long count;
      Node left, right, parent;

      public Node() {

      }
   }

   /************************************************************************************************************************************************/
   public static void main(String[] args) throws IOException {
      new Thread(null, new PlayOffTournament(), "1", 1 << 31).start();
   }

   static PrintWriter out = new PrintWriter(System.out);
   static Reader read = new Reader();
   static StringBuilder sbr = new StringBuilder();
   static int mod = (int) 1e9 + 7;
   static int dmax = Integer.MAX_VALUE;
   static long lmax = Long.MAX_VALUE;
   static int dmin = Integer.MIN_VALUE;
   static long lmin = Long.MIN_VALUE;
   static int[] dprimes = new int[] { 1, 11, 101, 1087, 99991, 100001, 1000003, 15485863, 999999937 };

   @Override
   public void run() {
      solve();
      out.close();
   }

   static class Reader {
      private byte[] buf = new byte[1024];
      private int index;
      private InputStream in;
      private int total;

      public Reader() {
         in = System.in;
      }

      public int scan() throws IOException {
         if (total < 0)
            throw new InputMismatchException();
         if (index >= total) {
            index = 0;
            total = in.read(buf);
            if (total <= 0)
               return -1;
         }
         return buf[index++];
      }

      public int intNext() throws IOException {
         int integer = 0;
         int n = scan();
         while (isWhiteSpace(n))
            n = scan();
         int neg = 1;
         if (n == '-') {
            neg = -1;
            n = scan();
         }
         while (!isWhiteSpace(n)) {
            if (n >= '0' && n <= '9') {
               integer *= 10;
               integer += n - '0';
               n = scan();
            } else
               throw new InputMismatchException();
         }
         return neg * integer;
      }

      public double doubleNext() throws IOException {
         double doub = 0;
         int n = scan();
         while (isWhiteSpace(n))
            n = scan();
         int neg = 1;
         if (n == '-') {
            neg = -1;
            n = scan();
         }
         while (!isWhiteSpace(n) && n != '.') {
            if (n >= '0' && n <= '9') {
               doub *= 10;
               doub += n - '0';
               n = scan();
            } else
               throw new InputMismatchException();
         }
         if (n == '.') {
            n = scan();
            double temp = 1;
            while (!isWhiteSpace(n)) {
               if (n >= '0' && n <= '9') {
                  temp /= 10;
                  doub += (n - '0') * temp;
                  n = scan();
               } else
                  throw new InputMismatchException();
            }
         }
         return doub * neg;
      }

      public String read() throws IOException {
         StringBuilder sb = new StringBuilder();
         int n = scan();
         while (isWhiteSpace(n))
            n = scan();
         while (!isWhiteSpace(n)) {
            sb.append((char) n);
            n = scan();
         }
         return sb.toString();
      }

      private boolean isWhiteSpace(int n) {
         if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1)
            return true;
         return false;
      }
   }

   static void print(Object object) {
      out.print(object);
   }

   static void println(Object object) {
      out.println(object);
   }

   static int[] iArr(int len) {
      return new int[len];
   }

   static long[] lArr(int len) {
      return new long[len];
   }

   static long min(long a, long b) {
      return Math.min(a, b);
   }

   static int min(int a, int b) {
      return Math.min(a, b);
   }

   static long max(Long a, Long b) {
      return Math.max(a, b);
   }

   static int max(int a, int b) {
      return Math.max(a, b);
   }

   static int ri() {
      try {
         return read.intNext();
      } catch (IOException e) {
         e.printStackTrace();
      }
      System.exit(2);
      return -1;
   }

   static long rl() {
      try {
         return Long.parseLong(read.read());
      } catch (IOException e) {
         e.printStackTrace();
      }
      System.exit(2);
      return -1;
   }

   static String rs() {
      try {
         return read.read();
      } catch (IOException e) {
         e.printStackTrace();
      }
      System.exit(2);
      return "";
   }

   static char rc() {
      return rs().charAt(0);
   }

   static double rd() {
      try {
         return read.doubleNext();
      } catch (IOException e) {
         e.printStackTrace();
      }
      System.exit(2);
      return -1;
   }
}