B'You have a bag of balls of n different colors. You have ai balls of the i-th color. While there are at least two different colored balls in the bag, perform the following steps: Let M xe2 x80 x89= xe2 x80 x89109 xe2 x80 x89+ xe2 x80 x897. It can be proven that the expected amount of time needed before you stop can be represented as a rational number , where P and Q are coprime integers and where Q is not divisible by M. Return the value . The first line of input will contain a single integer n (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n xe2 x80 x89 xe2 x89 xa4 xe2 x80 x892 xe2 x80 x89500) -- the number of colors. The next line of input will contain n space separated integers a1, xe2 x80 x89a2, xe2 x80 x89..., xe2 x80 x89an (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89ai xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89105) -- the number of balls of each color. Print a single integer, the answer to the problem. In the first sample, no matter what happens, the balls will become the same color after one step. For the second sample, we have 6 balls. Let xe2 x80 x99s label the balls from 1 to 6, and without loss of generality, let xe2 x80 x99s say balls 1,2,3 are initially color 1, balls 4,5 are color 2, and ball 6 are color 3. Here is an example of how these steps can go: It can be shown that the answer to this case is . '...