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 JAVA):

Solution:
//package com.company;

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

public class Main {
    public static class Task {
        int mod = 1000000007;
        int add(int a, int b) {
            int c = a + b;
            if (c >= mod) return c - mod;
            return c;
        }

        int mul(int a, int b) {
            return (int) ((long) a * b % mod);
        }

        int pow(int a, int b) {
            int r = 1;
            while (b > 0) {
                if (b % 2 == 1) r = mul(r, a);
                a = mul(a, a);
                b >>= 1;
            }
            return r;
        }


        int[] pow2;

        public class SegTree {

            public class NodeVal {
                int len, leftVal, rightVal, totVal;
                public NodeVal(int len, int ini) {
                    this.len = len;
                    leftVal = rightVal = ini;
                    totVal = 0;
                }
                void set(int len, int ini) {
                    this.len = len;
                    leftVal = rightVal = ini;
                }
                public void from(NodeVal left, NodeVal right) {
                    this.len = left.len + right.len;
                    this.leftVal = add(right.leftVal, mul(left.leftVal, pow2[right.len]));
                    this.rightVal = add(left.rightVal, mul(right.rightVal, pow2[left.len]));
                    this.totVal = add(mul(left.rightVal, right.leftVal),
                            add(mul(left.totVal, pow2[right.len]), mul(right.totVal, pow2[left.len])));
                }
            }
            NodeVal[] nodes;
            int T;
            public SegTree(int n) {
                T = 1;
                while (T < n) T <<= 1;
                nodes = new NodeVal[T << 1];
                for (int i = 0; i < T << 1; i++) {
                    nodes[i] = new NodeVal(0, 0);
                }
            }

            void update(int index, int len, int val) {
                nodes[index += T].set(len, val);
                while (index > 1) {
                    int parent = index >> 1;
                    int left = parent << 1;
                    int right = parent << 1 | 1;
                    nodes[parent].from(nodes[left], nodes[right]);
                    index >>= 1;
                }
            }
        }

        int solve(int[] strength) {
            int n = strength.length;
            Arrays.sort(strength);
            int ret = 0;
            for (int i = 0; i < n; i++) {
                int ps = 0;
                for (int j = i - 1; j >= 0; j--) {
                    ps = mul(ps, 2);
                    ps = add(ps, strength[j]);
                }
                ps = mul(ps, pow(2, n - 1 - i));
                int ss = 0;
                for (int j = i + 1; j < n; j++) {
                    ss = mul(ss, 2);
                    ss = add(ss, strength[j]);
                }
                ss = mul(ss, pow(2, i));
                ret = add(ret, mul(add(ps, ss), strength[i]));
            }
            return mul(ret, pow(pow(2, n + 1), mod - 2));
        }

        public class Pair {
            int a, b;

            public Pair(int a, int b) {
                this.a = a;
                this.b = b;
            }
        }

        public void solve(Scanner sc, PrintWriter pw) throws IOException {
            int n = sc.nextInt();
            int[] a = new int[n];
            int[] attachedIndex = new int[n];
            List<Pair> ps = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                a[i] = sc.nextInt();
                ps.add(new Pair(a[i], -(i + 1)));
            }
            int q = sc.nextInt();
            int[][] queries = new int[q][2];
            for (int i = 0; i < q; i++) {
                for (int j = 0; j < 2; j++) {
                    queries[i][j] = sc.nextInt();
                }
                queries[i][0]--;
                ps.add(new Pair(queries[i][1], i));
            }
            ps.sort(new Comparator<Pair>() {
                @Override
                public int compare(Pair o1, Pair o2) {
                    return o1.a - o2.a;
                }
            });
            int[] queryIndex = new int[q];
            int N = ps.size();
            for (int i = 0; i < N; i++) {
                if (ps.get(i).b < 0) {
                    attachedIndex[(-ps.get(i).b) - 1] = i;
                } else {
                    queryIndex[ps.get(i).b] = i;
                }
            }
            int inv2 = pow(pow(2, n), mod - 2);
            pow2 = new int[N + 1];
            pow2[0] = 1;
            for (int i = 1; i <= N; i++) {
                pow2[i] = mul(pow2[i - 1], 2);
            }
            SegTree st = new SegTree(N);
            for (int i = 0; i < n; i++) {
                st.update(attachedIndex[i], 1, a[i]);
            }
            int sol = mul(inv2, st.nodes[1].totVal);
//            System.err.println(Arrays.toString(attachedIndex));
//            System.err.println(sol);
//            System.err.println(solve(Arrays.copyOf(a, a.length)));
//            if (sol != solve(Arrays.copyOf(a, a.length))) throw new RuntimeException();
            pw.println(sol);
            for (int i = 0; i < q; i++) {
                int index = queries[i][0], value = queries[i][1];
                st.update(attachedIndex[index], 0, 0);
                st.update(attachedIndex[index] = queryIndex[i], 1, a[index] = value);
                sol = mul(inv2, st.nodes[1].totVal);
//                if (sol != solve(Arrays.copyOf(a, a.length))) throw new RuntimeException();
                pw.println(sol);
            }
        }
    }

    static long TIME_START, TIME_END;

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
//        Scanner sc = new Scanner(new FileInputStream("input"));
        PrintWriter pw = new PrintWriter(new BufferedOutputStream(System.out));
//        PrintWriter pw = new PrintWriter(new FileOutputStream("input"));

        Runtime runtime = Runtime.getRuntime();
        long usedMemoryBefore = runtime.totalMemory() - runtime.freeMemory();
        TIME_START = System.currentTimeMillis();
        Task t = new Task();
        t.solve(sc, pw);
        TIME_END = System.currentTimeMillis();
        long usedMemoryAfter = runtime.totalMemory() - runtime.freeMemory();
        pw.close();
        System.err.println("Memory increased: " + (usedMemoryAfter - usedMemoryBefore) / 1000000);
        System.err.println("Time used: " + (TIME_END - TIME_START) + ".");
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(FileReader s) throws FileNotFoundException {
            br = new BufferedReader(s);
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

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

        public String nextLine() throws IOException {
            return br.readLine();
        }

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

        public boolean ready() throws IOException {
            return br.ready();
        }
    }
}