Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

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

Sample Output 1

11
12
16

Initially, the sequence A is 1,2,3,4.

After each operation, it becomes the following:

2, 2, 3, 4

2, 2, 4, 4

4, 4, 4, 4

Sample Input 2

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

Sample Output 2

8
4
4

Note that the sequence A may not contain an element whose value is B_{i}.

Sample Input 3

2
1 2
3
1 100
2 100
100 1000

Sample Output 3

102
200
2000

Solution in Ruby (2.7.1) (judge verdict: Time Limit Exceeded)

def binary_search(key)
  l = 0; r = $a.size-1
  while l <= r
    mid = (l+r)/2
    if key == $a[mid]
      return mid
    end
    if key < $a[mid]
      r = mid - 1
    else
      l = mid + 1
    end
  end
end

def replace_same(key,ix,val)
  i = ix+1; j = ix-1
  $a[ix] = val
  while true
    if $a[i] == key && i < $a.size
      $a[i] = val
      i += 1
    else
      break
    end
  end
  while true
    if $a[j] == key && j >= 0
      $a[j] = val
      j -= 1
    else
      break
    end
  end
end

N = gets.to_i
$a = gets.split(" ").map(&:to_i)
Q = gets.to_i
b = []; c = []
Q.times do |i|
  b[i], c[i] = gets.split(" ").map(&:to_i)
end
$a.sort!
sum = $a.inject(0){|a,b|a+b}
Q.times do |q|
  rslt = binary_search(b[q])
  if rslt
    replace_same(b[q], rslt, c[q])
    $a.sort!
    sum = $a.inject(0){|a,b|a+b}
    puts sum
  else
    puts sum
  end
end