Problem: 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.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template <class T, class U>
using Pa = pair<T, U>;
template <class T>
using vec = vector<T>;
template <class T>
using vvec = vector<vec<T>>;
constexpr ll mod = 1e9 + 7;
struct mint {
  ll x;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  friend ostream& operator<<(ostream& os, const mint& a) { return os << a.x; }
  friend istream& operator>>(istream& is, mint& a) {
    ll t;
    is >> t;
    a = mint(t);
    return (is);
  }
  mint& operator+=(const mint a) {
    if ((x += a.x) >= mod) x -= mod;
    return *this;
  }
  mint& operator-=(const mint a) {
    if ((x += mod - a.x) >= mod) x -= mod;
    return *this;
  }
  mint& operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const {
    mint res(*this);
    return res += a;
  }
  mint operator-(const mint a) const {
    mint res(*this);
    return res -= a;
  }
  mint operator*(const mint a) const {
    mint res(*this);
    return res *= a;
  }
  mint pow(ll t) const {
    if (!t) return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1) a *= *this;
    return a;
  }
  mint inv() const { return pow(mod - 2); }
  mint& operator/=(const mint a) { return (*this) *= a.inv(); }
  mint operator/(const mint a) const {
    mint res(*this);
    return res /= a;
  }
};
template <typename Monoid, typename F>
class SegmentTree {
 private:
  int sz;
  vector<Monoid> seg;
  const F op;
  const Monoid e;

 public:
  SegmentTree(int n, const F op, const Monoid& e) : op(op), e(e) {
    sz = 1;
    while (sz <= n) sz <<= 1;
    seg.assign(2 * sz, e);
  }
  void set(int k, const Monoid& x) { seg[k + sz] = x; }
  void build() {
    for (int i = sz - 1; i > 0; i--) {
      seg[i] = op(seg[2 * i], seg[2 * i + 1]);
    }
  }
  void update(int k, const Monoid& x) {
    k += sz;
    seg[k] = x;
    while (k >>= 1) {
      seg[k] = op(seg[2 * k], seg[2 * k + 1]);
    }
  }
  Monoid query(int l, int r) {
    Monoid L = e, R = e;
    for (l += sz, r += sz; l < r; l >>= 1, r >>= 1) {
      if (l & 1) L = op(L, seg[l++]);
      if (r & 1) R = op(seg[--r], R);
    }
    return op(L, R);
  }
  Monoid operator[](const int& k) const { return seg[k + sz]; }
};
template <class T>
class Compress {
  map<T, int> idx;
  map<int, T> value;
  vector<T> cmp;

 public:
  int N;
  Compress(vector<T> v) {
    for (auto& x : v) cmp.push_back(x);
    sort(cmp.begin(), cmp.end());
    cmp.erase(unique(cmp.begin(), cmp.end()), cmp.end());
    N = cmp.size();
    for (int i = 0; i < N; i++) idx[cmp[i]] = i;
  }
  int id(T val) { return idx[val]; }
  T val(int id) { return cmp[id]; }
};
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int N;
  cin >> N;
  vec<mint> pow2(N + 1, 1);
  for (ll i = 1; i <= N; i++) pow2[i] = pow2[i - 1] * 2;
  mint two = 2;
  mint all = two.inv().pow(N);
  struct state {
    mint val, suml, sumr;
    ll num;
  };
  auto op = [&](state L, state R) {
    if (R.num == 0) return L;
    if (L.num == 0) return R;
    mint val = 0, suml = 0, sumr = 0;
    ll num = L.num + R.num;
    val = L.val * pow2[R.num] + R.val * pow2[L.num] + L.suml * R.sumr;
    suml = L.suml + R.suml * pow2[L.num];
    sumr = R.sumr + L.sumr * pow2[R.num];
    return (state){val, suml, sumr, num};
  };
  state e = (state){0, 0, 0, 0};
  vec<int> P(N);
  vec<Pa<Pa<int, int>, int>> v;
  for (int i = 0; i < N; i++) {
    cin >> P[i];
    v.push_back({{
                     P[i],
                     -1,
                 },
                 i});
  }
  int Q;
  cin >> Q;
  vec<int> A(Q), X(Q);
  for (int i = 0; i < Q; i++) {
    cin >> A[i] >> X[i];
    A[i]--;
    v.push_back({{X[i], i}, i});
  }
  vec<int> ida(Q);
  SegmentTree<state, decltype(op)> seg(N + Q, op, e);
  int id = 0;
  sort(v.begin(), v.end());
  vec<int> nid(N);
  for (auto& x : v) {
    if (x.first.second == -1) {
      ll a = x.first.first;
      seg.set(id, {0, a, a, 1});
      nid[x.second] = id;
    } else {
      ida[x.second] = id;
    }
    id++;
  }
  seg.build();
  auto answer = [&]() {
    state res = seg.query(0, N + Q);
    cout << res.val * all << "\n";
  };
  auto update = [&](int q) {
    int now = nid[A[q]];
    seg.update(now, e);
    nid[A[q]] = ida[q];
    seg.update(ida[q], {0, X[q], X[q], 1});
  };
  answer();
  for (int i = 0; i < Q; i++) {
    update(i);
    answer();
  }
}