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E. Mod Mod Mod

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a sequence of integers *a*_{1}, *a*_{2}, ..., *a*_{n}. 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 *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ 10^{13}) — the elements of the sequence.

Output

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

Examples

Input

2

10 5

Output

13

Input

5

5 4 3 2 1

Output

6

Input

4

5 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.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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