Integer Product

You are given N real values A_1, A_2, \ldots, A_N. Compute the number of pairs of indices (i, j) such that i < j and the product A_i \cdot A_j is integer.

Constraints

• 2 \leq N \leq 200,000
• 0 < A_i < 10^4
• A_i is given with at most 9 digits after the decimal.

Input

Input is given from Standard Input in the following format.

N A_1 A_2 \vdots A_N

Output

Print the number of pairs with integer product A_i \cdot A_j (and i < j).

Examples

Input

5 7.5 2.4 17.000000001 17 16.000000000

Output

3

Input

11 0.9 1 1 1.25 2.30000 5 70 0.000000001 9999.999999999 0.999999999 1.000000001

Output

8

inputFormat

Input

Input is given from Standard Input in the following format.

N A_1 A_2 \vdots A_N

outputFormat

Output

Print the number of pairs with integer product A_i \cdot A_j (and i < j).

Examples

Input

5 7.5 2.4 17.000000001 17 16.000000000

Output

3

Input

11 0.9 1 1 1.25 2.30000 5 70 0.000000001 9999.999999999 0.999999999 1.000000001

Output

8

样例

5
7.5
2.4
17.000000001
17
16.000000000

3