E. Mod Mod Modtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given a sequence of integers a1, a2, ..., an. Let , and  for 1 ≤ i < n. Here,  denotes the modulus operation. Find the maximum value of f(x, 1) over all nonnegative integers x. InputThe first line contains a single integer n (1 ≤ n ≤ 200000) — the length of the sequence.The second lines contains n integers a1, a2, ..., an (1 ≤ ai ≤ 1013) — the elements of the sequence.OutputOutput a single integer — the maximum value of f(x, 1) over all nonnegative integers x.ExamplesInput210 5Output13Input55 4 3 2 1Output6Input45 10 5 10Output16NoteIn the first example you can choose, for example, x = 19.In the second example you can choose, for example, x = 3 or x = 2.
Input210 5
Output13
['binary search', 'dp', 'math', '*3000']