Description

For any decimal fraction, we can obtain a set of approximations of different accuracy by mean of rounding. Take 0.2503 for example, we have the following approximations:

• 0.2503
• 0.250
• 0.25
• 0.3
• 0.

If two fractions A and B can both be rounded to C, we call C a common approximation of A and B. Two fractions may have more than one common approximations, each having a distinct accuracy. For example, 0.2503 and 0.2504 have common approximations 0.250 and 0.25. The accuracy of the former is 10⁻³, while that of the latter is 10⁻². Among all common approximations of two fractions, there is one that has the highest accuracy, and we call it the most accurate common approximation (MACA) of the two fractions. By this definition, the MACA of 0.2503 and 0.2504 is 0.250.

Given N fractions A_i (1 ≤ i ≤ N) in the range [0, 0.5), find a fraction x that maximizes the sum of −log₁₀ (the accuracy of the MACA of A_i and x). Report that maximized sum.

Input

The first line contains one integer N. N ≤ 100000.
Each of the next N lines contains a decimal fraction A_i. The total number of digits of the N decimal fractions doesn't exceed 400000. There is always a radix point, so zero is "0." instead of "0".

Output

One integer, the maximized sum.

4
0.250
0.2506
0.25115
0.2597

11

Hint

x = 0.25115.

Source

POJ Monthly--2007.11.25, Yang Yi