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E. Mod Mod Mod
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You 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.

Input

The 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.

Output

Output a single integer — the maximum value of f(x, 1) over all nonnegative integers x.

Examples
Input
210 5
Output
13
Input
55 4 3 2 1
Output
6
Input
45 10 5 10
Output
16
Note

In the first example you can choose, for example, x = 19.

In the second example you can choose, for example, x = 3 or x = 2.