You are given a function:

$$\displaystyle f(x) = \begin{cases} x & \text{if } (x-1)!+1 \equiv 0\pmod x \\ -x & \text{if } (x-1)!+1 \not\equiv 0\pmod x \end{cases}$$

where ~!~ denotes the factorial operation. In other words, the function returns ~x~ if ~(x-1)!+1~ is divisible by ~x~, and ~-x~ otherwise.

Given an array ~a~, print out the minimum value of ~f(x)~ for all elements in ~a~.

Input Specification

The first line will contain the integer ~N~ ~(1 \le N \le 10^5)~.

The second line will contain ~N~ integers, ~a_1, a_2, \ldots, a_N~ ~(2 \le a_i \le 10^6)~.

Output Specification

Print the minimum value of ~f(x)~ for all elements in ~a~.

Scoring

Let ~L~ represent the number of characters in your solution.

If ~L~ is less than ~160~, your score will be ~\min (1, 1-\frac{L-137}{40}) \times 100\%~.

If ~L~ is greater than or equal to ~160~, and less than ~1~ ~000~, your score is ~(\frac{150}{L})^2 \times 50\%~.

Otherwise, your score is ~0~.

Sample Input

8
2 5 3 9 3 5 7 12

Sample Output

-12