#include <bits/stdc++.h>
using namespace std;
template <class T1, class T2>
ostream& operator<<(ostream& out, pair<T1, T2> p) {
  out << '(' << p.first << ',' << p.second << ')';
  return out;
}
template <class T1, class T2>
istream& operator>>(istream& in, pair<T1, T2>& p) {
  in >> p.first >> p.second;
  return in;
}
template <class T>
istream& operator>>(istream& in, vector<T>& v) {
  for (T& x : v) in >> x;
  return in;
}
template <class T>
ostream& operator<<(ostream& out, vector<vector<T>>& v) {
  for (vector<T>& x : v) out << x << '\n';
  return out;
}
template <class T>
ostream& operator<<(ostream& out, vector<T>& v) {
  for (T& x : v) out << x << ' ';
  return out;
}
long long gcd(long long a, long long b) {
  if (b > a) swap(a, b);
  return (b ? gcd(b, a % b) : a);
}
using ll = long long;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
using tiii = pair<pair<int, int>, int>;
using vi = vector<int>;
using vl = vector<long long>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
const int h = 1000000007;
vl pw(300001);
long long p(long long x, long long y) {
  static const int mod = 1000000007;
  if (y == 0) return 1;
  long long z = p(x, y / 2);
  z *= z;
  z %= mod;
  return (y & 1 ? (z * x) % mod : z);
}
long long inv(long long x) {
  static const int mod = 1000000007;
  return p(x, mod - 2);
}
struct elem {
  ll val;
  ll Lval;
  ll Rval;
  ll count;
};
template <class T = long long>
class SegTree {
 private:
  T default_element_value{0, 0, 0, 0};
  vector<T> v, seg_tree;
  T merge(T x, T y) {
    elem res;
    res.val = (x.val * pw[y.count]) % h + (y.val * pw[x.count]) % h +
              (x.Lval * y.Rval) % h;
    res.val %= h;
    res.Lval = (x.Lval + y.Lval * pw[x.count]) % h;
    res.Rval = (y.Rval + x.Rval * pw[y.count]) % h;
    res.count = x.count + y.count;
    return res;
  }
  void build(int node, int start, int end) {
    if (start == end)
      seg_tree[node] = v[start];
    else {
      build(2 * node + 1, start, (start + end) / 2);
      build(2 * node + 2, (start + end) / 2 + 1, end);
      seg_tree[node] = merge(seg_tree[2 * node + 1], seg_tree[2 * node + 2]);
    }
  }
  void update(int node, int start, int end, int index, T val) {
    if (start == end) {
      seg_tree[node] = val;
      return;
    }
    if (index <= (start + end) / 2)
      update(2 * node + 1, start, (start + end) / 2, index, val);
    else
      update(2 * node + 2, (start + end) / 2 + 1, end, index, val);
    seg_tree[node] = merge(seg_tree[2 * node + 1], seg_tree[2 * node + 2]);
  }
  T query(int node, int start, int end, int l, int r) {
    if (end < l || start > r) return default_element_value;
    if (start >= l && end <= r) return seg_tree[node];
    return merge(query(2 * node + 1, start, (start + end) / 2, l, r),
                 query(2 * node + 2, (start + end) / 2 + 1, end, l, r));
  }

 public:
  SegTree(int n) {
    v.resize(n, default_element_value);
    seg_tree.resize(4 * n, default_element_value);
  }
  SegTree(vector<T>& arr) {
    v = arr;
    seg_tree.resize(4 * v.size(), default_element_value);
    build(0, 0, v.size() - 1);
  }
  void update(int index, T val) { update(0, 0, v.size() - 1, index, val); }
  T query(int l, int r) { return query(0, 0, v.size() - 1, l, r); }
};
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  cerr.setstate(ios::failbit);
  pw[0] = 1;
  for (int i = 1; i < pw.size(); i++) pw[i] = pw[i - 1] * 2 % h;
  int n;
  cin >> n;
  vl p(n);
  cin >> p;
  int q;
  cin >> q;
  vector<pll> queries(q);
  cin >> queries;
  vl v(p);
  for (auto p : queries) v.push_back(p.second);
  sort(v.begin(), v.end());
  map<ll, ll> index;
  for (int i = 0; i < v.size(); i++) {
    if (!index.count(v[i])) index[v[i]] = i;
  }
  SegTree<elem> seg(v.size());
  map<ll, ll> del = index;
  for (int x : p) seg.update(index[x]++, elem({0, x, x, 1}));
  cout << seg.query(0, v.size() - 1).val * inv(pw[p.size()]) % h << '\n';
  for (auto x : queries) {
    seg.update(del[p[x.first - 1]], elem({0, 0, 0, 0}));
    del[p[x.first - 1]]++;
    p[x.first - 1] = x.second;
    seg.update(index[x.second]++, elem({0, x.second, x.second, 1}));
    cout << seg.query(0, v.size() - 1).val * inv(pw[p.size()]) % h << '\n';
  }
}

### Prompt

Develop a solution in Cpp to the problem described below:

There are n officers in the Army of Byteland. Each officer has some power associated with him. The power of the i-th officer is denoted by p_{i}. As the war is fast approaching, the General would like to know the strength of the army.

The strength of an army is calculated in a strange way in Byteland. The General selects a random subset of officers from these n officers and calls this subset a battalion.(All 2^n subsets of the n officers can be chosen equally likely, including empty subset and the subset of all officers).

The strength of a battalion is calculated in the following way:

Let the powers of the chosen officers be a_{1},a_{2},…,a_{k}, where a_1 ≤ a_2 ≤ ... ≤ a_k. The strength of this battalion is equal to a_1a_2 + a_2a_3 + ... + a_{k-1}a_k. (If the size of Battalion is ≤ 1, then the strength of this battalion is 0).

The strength of the army is equal to the expected value of the strength of the battalion.

As the war is really long, the powers of officers may change. Precisely, there will be q changes. Each one of the form i x indicating that p_{i} is changed to x.

You need to find the strength of the army initially and after each of these q updates.

Note that the changes are permanent.

The strength should be found by modulo 10^{9}+7. Formally, let M=10^{9}+7. It can be shown that the answer can be expressed as an irreducible fraction p/q, where p and q are integers and qnot≡ 0 mod M). Output the integer equal to p⋅ q^{-1} mod M. In other words, output such an integer x that 0 ≤ x < M and x ⋅ q ≡ p mod M).

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 3⋅10^{5}) — the number of officers in Byteland's Army.

The second line contains n integers p_{1},p_{2},…,p_{n} (1 ≤ p_{i} ≤ 10^{9}).

The third line contains a single integer q (1 ≤ q ≤ 3⋅10^{5}) — the number of updates.

Each of the next q lines contains two integers i and x (1 ≤ i ≤ n,  1 ≤ x ≤ 10^{9}), indicating that p_{i} is updated to x .

Output

In the first line output the initial strength of the army.

In i-th of the next q lines, output the strength of the army after i-th update.

Examples

Input


2
1 2
2
1 2
2 1


Output


500000004
1
500000004


Input


4
1 2 3 4
4
1 5
2 5
3 5
4 5


Output


625000011
13
62500020
375000027
62500027

Note

In first testcase, initially, there are four possible battalions 

  * {} Strength = 0 
  * {1} Strength = 0 
  * {2} Strength = 0 
  * {1,2} Strength = 2 

So strength of army is (0+0+0+2)/(4) = 1/2

After changing p_{1} to 2, strength of battallion {1,2} changes to 4, so strength of army becomes 1.

After changing p_{2} to 1, strength of battalion {1,2} again becomes 2, so strength of army becomes 1/2.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <class T1, class T2>
ostream& operator<<(ostream& out, pair<T1, T2> p) {
  out << '(' << p.first << ',' << p.second << ')';
  return out;
}
template <class T1, class T2>
istream& operator>>(istream& in, pair<T1, T2>& p) {
  in >> p.first >> p.second;
  return in;
}
template <class T>
istream& operator>>(istream& in, vector<T>& v) {
  for (T& x : v) in >> x;
  return in;
}
template <class T>
ostream& operator<<(ostream& out, vector<vector<T>>& v) {
  for (vector<T>& x : v) out << x << '\n';
  return out;
}
template <class T>
ostream& operator<<(ostream& out, vector<T>& v) {
  for (T& x : v) out << x << ' ';
  return out;
}
long long gcd(long long a, long long b) {
  if (b > a) swap(a, b);
  return (b ? gcd(b, a % b) : a);
}
using ll = long long;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
using tiii = pair<pair<int, int>, int>;
using vi = vector<int>;
using vl = vector<long long>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
const int h = 1000000007;
vl pw(300001);
long long p(long long x, long long y) {
  static const int mod = 1000000007;
  if (y == 0) return 1;
  long long z = p(x, y / 2);
  z *= z;
  z %= mod;
  return (y & 1 ? (z * x) % mod : z);
}
long long inv(long long x) {
  static const int mod = 1000000007;
  return p(x, mod - 2);
}
struct elem {
  ll val;
  ll Lval;
  ll Rval;
  ll count;
};
template <class T = long long>
class SegTree {
 private:
  T default_element_value{0, 0, 0, 0};
  vector<T> v, seg_tree;
  T merge(T x, T y) {
    elem res;
    res.val = (x.val * pw[y.count]) % h + (y.val * pw[x.count]) % h +
              (x.Lval * y.Rval) % h;
    res.val %= h;
    res.Lval = (x.Lval + y.Lval * pw[x.count]) % h;
    res.Rval = (y.Rval + x.Rval * pw[y.count]) % h;
    res.count = x.count + y.count;
    return res;
  }
  void build(int node, int start, int end) {
    if (start == end)
      seg_tree[node] = v[start];
    else {
      build(2 * node + 1, start, (start + end) / 2);
      build(2 * node + 2, (start + end) / 2 + 1, end);
      seg_tree[node] = merge(seg_tree[2 * node + 1], seg_tree[2 * node + 2]);
    }
  }
  void update(int node, int start, int end, int index, T val) {
    if (start == end) {
      seg_tree[node] = val;
      return;
    }
    if (index <= (start + end) / 2)
      update(2 * node + 1, start, (start + end) / 2, index, val);
    else
      update(2 * node + 2, (start + end) / 2 + 1, end, index, val);
    seg_tree[node] = merge(seg_tree[2 * node + 1], seg_tree[2 * node + 2]);
  }
  T query(int node, int start, int end, int l, int r) {
    if (end < l || start > r) return default_element_value;
    if (start >= l && end <= r) return seg_tree[node];
    return merge(query(2 * node + 1, start, (start + end) / 2, l, r),
                 query(2 * node + 2, (start + end) / 2 + 1, end, l, r));
  }

 public:
  SegTree(int n) {
    v.resize(n, default_element_value);
    seg_tree.resize(4 * n, default_element_value);
  }
  SegTree(vector<T>& arr) {
    v = arr;
    seg_tree.resize(4 * v.size(), default_element_value);
    build(0, 0, v.size() - 1);
  }
  void update(int index, T val) { update(0, 0, v.size() - 1, index, val); }
  T query(int l, int r) { return query(0, 0, v.size() - 1, l, r); }
};
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  cerr.setstate(ios::failbit);
  pw[0] = 1;
  for (int i = 1; i < pw.size(); i++) pw[i] = pw[i - 1] * 2 % h;
  int n;
  cin >> n;
  vl p(n);
  cin >> p;
  int q;
  cin >> q;
  vector<pll> queries(q);
  cin >> queries;
  vl v(p);
  for (auto p : queries) v.push_back(p.second);
  sort(v.begin(), v.end());
  map<ll, ll> index;
  for (int i = 0; i < v.size(); i++) {
    if (!index.count(v[i])) index[v[i]] = i;
  }
  SegTree<elem> seg(v.size());
  map<ll, ll> del = index;
  for (int x : p) seg.update(index[x]++, elem({0, x, x, 1}));
  cout << seg.query(0, v.size() - 1).val * inv(pw[p.size()]) % h << '\n';
  for (auto x : queries) {
    seg.update(del[p[x.first - 1]], elem({0, 0, 0, 0}));
    del[p[x.first - 1]]++;
    p[x.first - 1] = x.second;
    seg.update(index[x.second]++, elem({0, x.second, x.second, 1}));
    cout << seg.query(0, v.size() - 1).val * inv(pw[p.size()]) % h << '\n';
  }
}

```