Replacing

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

inputFormat

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}

outputFormat

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

样例

2
1 2
3
1 100
2 100
100 1000

102
200
2000

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