#include <bits/stdc++.h>
#define ff first
#define ss second
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define repi(n) for(int i = 0; i < (n); i++)
#define rep(i, n) for(int (i) = 0; (i) < (n); (i)++)
#define all(p) p.begin(), p.end()
#define a_count(p) __builtin_acountll(p)
#define len(s, e) ((e)-(s)+1)
#define mid(s, e) ((s)+((e)-(s))/2)
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<int, ll> pil;
typedef pair<ll, int> pli;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
const int mod = 1e9 + 7;
const int oo = 1e9;
const ll OO = 1e18;
#ifdef ONLINE_JUDGE
#define endl '\n'
#endif
template <typename A, typename B>
istream& operator >>(istream& in, pair<A, B>& a) {
	in >> a.first >> a.second;
    return in;
}
template <typename T>
istream& operator >>(istream& in, vector<T>& a) {
    for (auto& v : a) in >> v;
    return in;
}
template <typename T, size_t N>
istream& operator >>(istream& in, array<T, N>& a) {
    for (size_t i = 0; i < N; i++) in >> a[i];
    return in;
}
#ifdef ANEEE_LOCAL
template <typename A, typename B>
ostream& operator <<(ostream& out, const pair<A, B>& a) {
    out << "(" << a.first << "," << a.second << ")";
    return out;
}
template <typename T>
ostream& operator <<(ostream& out, const vector<T>& a) {
    out << "["; bool first = true;
    for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]";
    return out;
}
template <typename T, size_t N>
ostream& operator <<(ostream& out, const array<T, N>& a) {
    out << "["; bool first = true;
    for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]";
    return out;
}
template <typename T, class Cmp>
ostream& operator <<(ostream& out, const set<T, Cmp>& a) {
    out << "{"; bool first = true;
    for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "}";
    return out;
}
template <typename U, typename T, class Cmp>
ostream& operator <<(ostream& out, const map<U, T, Cmp>& a) {
    out << "{"; bool first = true;
    for (auto& p : a) { out << (first ? "" : ", "); out << p.first << ":" << p.second; first = 0;} out << "}";
    return out;
}
template <typename T>
ostream& operator <<(ostream& out, const list<T>& a) {
    out << "["; bool first = true;
    for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]";
    return out;
}
#else
template <typename A, typename B>
ostream& operator <<(ostream& out, const pair<A, B>& a) {
    out << a.first << " " << a.second;
    return out;
}
template <typename T>
ostream& operator <<(ostream& out, const vector<T>& a) {
    auto n = a.size();
    for (auto i = 0; i < n; i++) {
        cout << a[i];
        if (i != n-1) cout << '.';
    }
    return out;
}
template <typename T, size_t N>
ostream& operator <<(ostream& out, const array<T, N>& a) {
    for (auto& v : a) out << v << ' ';
    return out;
}
template <typename T, class Cmp>
ostream& operator <<(ostream& out, const set<T, Cmp>& a) {
    for (auto& v : a) out << v << ' ';
    return out;
}
template <typename U, typename T, class Cmp>
ostream& operator <<(ostream& out, const map<U, T, Cmp>& a) {
    for (auto& p : a) out << p << '\n';
    return out;
}
template <typename T>
ostream& operator <<(ostream& out, const list<T>& a) {
    for (auto& v : a) out << v << ' ';
    return out;
}
#endif
#ifdef ANEEE_LOCAL
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
#else
#define trace(...) 7
#endif
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
	cerr <<"[" << name << ": " << arg1 << "]" << endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
    const char* comma = strchr(names + 1, ',');
    cerr << "[";
    cerr.write(names, comma - names) << ": " << arg1 << "]  ";
    __f(comma + 2, args...);
}
template <typename Arg1>
void print(Arg1&& arg1){
	cout << arg1 << endl;
}
template <typename Arg1, typename... Args>
void print(Arg1&& arg1, Args&&... args){
    cout << arg1 << ' ';
    print(args...);
}
template <typename Arg1>
void read(Arg1&& arg1){
	cin >> arg1;
}
template <typename Arg1, typename... Args>
void read(Arg1&& arg1, Args&&... args){
    cin >> arg1;
    read(args...);
}
int nextInt() { int x; read(x); return x; }
ll nextLong() { ll x; read(x); return x; }

class Timer {
	string _name;
	clock_t _start;
public:
	Timer(string name = "Runtime") { _name = "["+name+": ", _start = clock(); }
	~Timer() { cerr << _name << double(clock() - _start)/CLOCKS_PER_SEC << "]\n"; }
};

inline void precomp() {}

void solve() {
    int kk;
    read(kk);
    int n = 1 << kk;
    vector<ll> tree(n << 1);
    string s;
    read(s);
    map<int, int> node, invnode;
    for (int i = 0; i < n; i++) tree[n + i] = 1;
    for (int i = n - 1, k = 0; i > 0; i--, k++) {
        node[k] = i;
        invnode[i] = k;
        switch(s[k]) {
            case '0':
            tree[i] = tree[i << 1 | 1];
            break;
            case '1':
            tree[i] = tree[i << 1];
            break;
            case '?':
            tree[i] = tree[i << 1] + tree[i << 1 | 1];
            break;
        }
    }
    ll q;
    read(q);
    while(q--) {
        int p;
        char c;
        read(p, c);
        p--;
        s[p] = c;
        int i = node[p];
        while (i) {
            switch(s[p]) {
                case '0':
                tree[i] = tree[i << 1 | 1];
                break;
                case '1':
                tree[i] = tree[i << 1];
                break;
                case '?':
                tree[i] = tree[i << 1] + tree[i << 1 | 1];
                break;
            }
            i >>= 1;
            p = invnode[i];
        }
        print(tree[1]);
    }
}

signed main() {
	Timer ti;
	ios_base::sync_with_stdio(false);
	cin.tie(nullptr); cout.tie(nullptr);
	int T = 1;
	#ifdef TEST_CASES
	cin >> T;
	#endif
    precomp();
	for(int tt = 1; tt <= T; tt++) {
		#ifdef CASE_INFO
		cout << "Case #" << tt << ": ";
		#endif
		solve();
	}
	return 0;
}
### Prompt

Construct a CPP code solution to the problem outlined:

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

### Response

```cpp
#include <bits/stdc++.h>
#define ff first
#define ss second
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define repi(n) for(int i = 0; i < (n); i++)
#define rep(i, n) for(int (i) = 0; (i) < (n); (i)++)
#define all(p) p.begin(), p.end()
#define a_count(p) __builtin_acountll(p)
#define len(s, e) ((e)-(s)+1)
#define mid(s, e) ((s)+((e)-(s))/2)
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<int, ll> pil;
typedef pair<ll, int> pli;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
const int mod = 1e9 + 7;
const int oo = 1e9;
const ll OO = 1e18;
#ifdef ONLINE_JUDGE
#define endl '\n'
#endif
template <typename A, typename B>
istream& operator >>(istream& in, pair<A, B>& a) {
	in >> a.first >> a.second;
    return in;
}
template <typename T>
istream& operator >>(istream& in, vector<T>& a) {
    for (auto& v : a) in >> v;
    return in;
}
template <typename T, size_t N>
istream& operator >>(istream& in, array<T, N>& a) {
    for (size_t i = 0; i < N; i++) in >> a[i];
    return in;
}
#ifdef ANEEE_LOCAL
template <typename A, typename B>
ostream& operator <<(ostream& out, const pair<A, B>& a) {
    out << "(" << a.first << "," << a.second << ")";
    return out;
}
template <typename T>
ostream& operator <<(ostream& out, const vector<T>& a) {
    out << "["; bool first = true;
    for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]";
    return out;
}
template <typename T, size_t N>
ostream& operator <<(ostream& out, const array<T, N>& a) {
    out << "["; bool first = true;
    for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]";
    return out;
}
template <typename T, class Cmp>
ostream& operator <<(ostream& out, const set<T, Cmp>& a) {
    out << "{"; bool first = true;
    for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "}";
    return out;
}
template <typename U, typename T, class Cmp>
ostream& operator <<(ostream& out, const map<U, T, Cmp>& a) {
    out << "{"; bool first = true;
    for (auto& p : a) { out << (first ? "" : ", "); out << p.first << ":" << p.second; first = 0;} out << "}";
    return out;
}
template <typename T>
ostream& operator <<(ostream& out, const list<T>& a) {
    out << "["; bool first = true;
    for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]";
    return out;
}
#else
template <typename A, typename B>
ostream& operator <<(ostream& out, const pair<A, B>& a) {
    out << a.first << " " << a.second;
    return out;
}
template <typename T>
ostream& operator <<(ostream& out, const vector<T>& a) {
    auto n = a.size();
    for (auto i = 0; i < n; i++) {
        cout << a[i];
        if (i != n-1) cout << '.';
    }
    return out;
}
template <typename T, size_t N>
ostream& operator <<(ostream& out, const array<T, N>& a) {
    for (auto& v : a) out << v << ' ';
    return out;
}
template <typename T, class Cmp>
ostream& operator <<(ostream& out, const set<T, Cmp>& a) {
    for (auto& v : a) out << v << ' ';
    return out;
}
template <typename U, typename T, class Cmp>
ostream& operator <<(ostream& out, const map<U, T, Cmp>& a) {
    for (auto& p : a) out << p << '\n';
    return out;
}
template <typename T>
ostream& operator <<(ostream& out, const list<T>& a) {
    for (auto& v : a) out << v << ' ';
    return out;
}
#endif
#ifdef ANEEE_LOCAL
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
#else
#define trace(...) 7
#endif
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
	cerr <<"[" << name << ": " << arg1 << "]" << endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
    const char* comma = strchr(names + 1, ',');
    cerr << "[";
    cerr.write(names, comma - names) << ": " << arg1 << "]  ";
    __f(comma + 2, args...);
}
template <typename Arg1>
void print(Arg1&& arg1){
	cout << arg1 << endl;
}
template <typename Arg1, typename... Args>
void print(Arg1&& arg1, Args&&... args){
    cout << arg1 << ' ';
    print(args...);
}
template <typename Arg1>
void read(Arg1&& arg1){
	cin >> arg1;
}
template <typename Arg1, typename... Args>
void read(Arg1&& arg1, Args&&... args){
    cin >> arg1;
    read(args...);
}
int nextInt() { int x; read(x); return x; }
ll nextLong() { ll x; read(x); return x; }

class Timer {
	string _name;
	clock_t _start;
public:
	Timer(string name = "Runtime") { _name = "["+name+": ", _start = clock(); }
	~Timer() { cerr << _name << double(clock() - _start)/CLOCKS_PER_SEC << "]\n"; }
};

inline void precomp() {}

void solve() {
    int kk;
    read(kk);
    int n = 1 << kk;
    vector<ll> tree(n << 1);
    string s;
    read(s);
    map<int, int> node, invnode;
    for (int i = 0; i < n; i++) tree[n + i] = 1;
    for (int i = n - 1, k = 0; i > 0; i--, k++) {
        node[k] = i;
        invnode[i] = k;
        switch(s[k]) {
            case '0':
            tree[i] = tree[i << 1 | 1];
            break;
            case '1':
            tree[i] = tree[i << 1];
            break;
            case '?':
            tree[i] = tree[i << 1] + tree[i << 1 | 1];
            break;
        }
    }
    ll q;
    read(q);
    while(q--) {
        int p;
        char c;
        read(p, c);
        p--;
        s[p] = c;
        int i = node[p];
        while (i) {
            switch(s[p]) {
                case '0':
                tree[i] = tree[i << 1 | 1];
                break;
                case '1':
                tree[i] = tree[i << 1];
                break;
                case '?':
                tree[i] = tree[i << 1] + tree[i << 1 | 1];
                break;
            }
            i >>= 1;
            p = invnode[i];
        }
        print(tree[1]);
    }
}

signed main() {
	Timer ti;
	ios_base::sync_with_stdio(false);
	cin.tie(nullptr); cout.tie(nullptr);
	int T = 1;
	#ifdef TEST_CASES
	cin >> T;
	#endif
    precomp();
	for(int tt = 1; tt <= T; tt++) {
		#ifdef CASE_INFO
		cout << "Case #" << tt << ": ";
		#endif
		solve();
	}
	return 0;
}
```