Problem: You have a sequence A composed of N positive integers: A_{1}, A_{2}, \cdots, A_{N}.

You will now successively do the following Q operations:

* In the i-th operation, you replace every element whose value is B_{i} with C_{i}.



For each i (1 \leq i \leq Q), find S_{i}: the sum of all elements in A just after the i-th operation.

Constraints

* All values in input are integers.
* 1 \leq N, Q, A_{i}, B_{i}, C_{i} \leq 10^{5}
* B_{i} \neq C_{i}

Input

Input is given from Standard Input in the following format:


N
A_{1} A_{2} \cdots A_{N}
Q
B_{1} C_{1}
B_{2} C_{2}
\vdots
B_{Q} C_{Q}


Output

Print Q integers S_{i} to Standard Output in the following format:


S_{1}
S_{2}
\vdots
S_{Q}


Note that S_{i} may not fit into a 32-bit integer.

Examples

Input

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


Output

11
12
16


Input

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


Output

8
4
4


Input

2
1 2
3
1 100
2 100
100 1000


Output

102
200
2000

Solution (in JAVA):

Solution:
import java.util.Scanner;
import java.util.Arrays;

public class Main {
  
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    
    //与えられる値群を配列ではなくインデックス番号として解釈する
    int[] A = new int[100001];
    long sum = 0;
    for (int i = 0; i < N; i++) {
      int a = sc.nextInt(); //値取得
      A[a] += 1; //該当インデックスの値の個数
      sum += a; //与えられた値群の合計
    }
    
    int Q = sc.nextInt();
    
    for (int i = 0; i < Q; i++) {
      int target = sc.nextInt(); //置換対象
      int value = sc.nextInt(); //置換先
      
      A[value] = A[value] + A[target]; //置換対象の値の個数を、置換先にマージ
      sum += (value - target) * A[target]; //合計値への影響は、(置換先-置換対象の差)×置換対象の値の個数
      
      A[target] = 0; //置換しちゃったので値がもうない
      System.out.println(sum);
    }
  }
}