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

public class Main {
    //input
    static out op = new out();
    static inp ip = new inp();
    static FastReader sc = new FastReader();
    static BufferedWriter output = new BufferedWriter( 
        new OutputStreamWriter(System.out));
   
    //HashMap<Integer,Integer> map = new HashMap<>();

    
    static void sol() throws Exception{
        int k = ip.in();
        char[] str = ip.cain();

        int n = str.length;

        char[] st = new char[n+1];

        for(int i=0;i<n;i++){
            st[n-i] = str[i];
        }
        Node root = new Node();
        root = buildSt(st,root,1,n);

        calc(root);
        //op.sbln(root.val);
        
        // display(root);
        // op.sbln("");

        int q = ip.in();
        while(q-- > 0){
            int p = ip.in();
            char c = ip.cin();
            Stack<Integer> s = new Stack<>();
        
            pathfind(s,n-p+1);
            update(s,root,c);

            // display(root);
            // op.sbln("");
            
            op.sbln(root.val);
        }
    }
    static void display(Node root){
        Queue<Node> q = new LinkedList<>();
        q.add(root);
        while(!q.isEmpty()){
            Node v = q.remove();
            System.out.print(v.data);
            if(v.left != null)
                q.add(v.left);
            if(v.right != null)
                q.add(v.right);
        }
    }
    static void update(Stack<Integer> s,Node root, char c) {
        if(s.size()<=1){
            //System.out.println(root.data+" "+root.ind);
            root.data = c;
            if(root.left != null && root.right!=null){
                if(c=='1')root.val = root.left.val;
                else if(c == '0') root.val = root.right.val;
                else root.val = root.left.val + root.right.val;
            }
            else{
                if(c == '?')root.val = 2;
                else root.val = 1;
            }

            return;
            
        }
        int v = s.pop();
        if(s.peek() == 2*v)update(s, root.left, c);
        else update(s, root.right, c);

        if(root.left != null && root.right!=null){
                if(root.data=='1')root.val = root.left.val;
                else if(root.data == '0') root.val = root.right.val;
                else root.val = root.left.val + root.right.val;
        }
        else{
            if(c == '?')root.val = 2;
            else root.val = 1;
        }
    }

    static void pathfind(Stack<Integer> s, int p) {
        if(p<1)return;
        s.push(p);
        pathfind(s, p/2);
    }

    static void calc(Node root){
        if(root == null)return;

        calc(root.left);
        calc(root.right);

        if(root.left == null && root.right==null){
            if(root.data == '?')root.val = 2;
            else root.val = 1;
            
            return;
        }else{
            if(root.data =='1')root.val = root.left.val;
            else if(root.data  == '0') root.val = root.right.val;
            else root.val = root.left.val + root.right.val;
        }

    }
    static Node buildSt(char[] st,Node root,int i,int n){
        if(i<=n){

            Node temp = new Node(st[i]);
            root = temp;
            
            root.left = buildSt(st,root.left,2*i,n);
            root.right = buildSt(st,root.right,2*i+1,n);
        }

        return root;
    }
    public static void main(String[] args) throws Exception { 
        // int t = ip.in();
        // while(t-- > 0){
             sol();
        // }
        op.output.flush();
    }
    

    public static long gcd(long a,long b) {
        if(b==0){
            return a;
        }
        return gcd(b,a%b);
    }

    static class Node /*implements Comparable<Node>*/{
        char data;
        int val;
        Node left,right;
        Node(){
    
        }
        Node(char ch){
            data = ch;
            left = null;
            right = null;
        }
    
        // @Override
        // // public int compareTo(Node o) {
        // //     if(this.data == o.data)
        // //     return this.ind - o.ind;
        // //     // TODO Auto-generated method stub
        // //     return o.data - this.data;
        // // }
    }
}


class FastReader 
{ 
    BufferedReader br; 
    StringTokenizer st; 

    public FastReader() 
    { 
        br = new BufferedReader(new
                 InputStreamReader(System.in)); 
    } 

    String next() 
    { 
        while (st == null || !st.hasMoreElements()) 
        { 
            try
            { 
                st = new StringTokenizer(br.readLine()); 
            } 
            catch (IOException  e) 
            { 
                e.printStackTrace(); 
            } 
        } 
        return st.nextToken(); 
    } 

    int nextInt() 
    { 
        return Integer.parseInt(next()); 
    } 

    long nextLong() 
    { 
        return Long.parseLong(next()); 
    } 

    double nextDouble() 
    { 
        return Double.parseDouble(next()); 
    } 

    String nextLine() 
    { 
        String str = ""; 
        try
        { 
            str = br.readLine(); 
        } 
        catch (IOException e) 
        { 
            e.printStackTrace(); 
        } 
        return str; 
    }

}
class inp{
    FastReader sc = new FastReader();
    int in(){
        int a = sc.nextInt();
        return a;
    }
    long lin(){
        long a = sc.nextLong();
        return a;
    }
    char cin(){
        char c = sc.next().charAt(0);
        return c;
    }
    char[] cain(){
        char[] a = sc.nextLine().toCharArray();
        return a;
    }
    int[] arrin(int n){
        int [] arr = new int[n];
        for(int i=0;i<n;i++)
            arr[i] = in();

        return arr;
    }
    int[] mm_arr(int[] arr){
        int max = Integer.MIN_VALUE;
        int min = Integer.MAX_VALUE;
        for(int i=0;i<arr.length;i++){
            max = Math.max(max,arr[i]);
            min = Math.min(min,arr[i]);
        }
        int ans[] = {max,min};
        return ans;
    }
    int[] srt(int[] arr){
        Arrays.sort(arr);
        return arr;
    }
    long pow(long a,long b){
        if(b == 0)return 1;
        long res = pow(a,b/2);
        //System.out.println(res + " " + b + " " + (b&1));
        if((b&1) == 0)return res*res;
        return a*res*res; 
    }

    boolean[] prime(){
        boolean prime[] = new boolean[100000001];
        Arrays.fill(prime,true);
        for (int p = 2; p * p <= 10000000; p++)
        {
            // If prime[p] is not changed,
            // then it is a prime
            if (prime[p] == true)
            {
                // Update all multiples
                // of p greater than or
                // equal to the square of it
                // numbers which are multiple
                // of p and are less than p^2
                // are already been marked.
                for (int i = p * p; i <= 10000000; i += p)
                    prime[i] = false;
            }
        }
        return prime;
    }
}
class out{
    BufferedWriter output = new BufferedWriter( 
        new OutputStreamWriter(System.out)); 

    void sb(String s) throws IOException {
        output.write(s);
    }
    void sbln(Object s) throws IOException {
        output.write(s+"\n");
    }
}