#include <bits/stdc++.h>
using namespace std;
int n;
long long arr2[200020], arr1[200020];
int main() {
  long long a, b;
  cin >> n;
  for (int i = n; i; i--) {
    long long c;
    cin >> c;
    arr1[i] = c;
  }
  for (int i = n - 1; i; i--) arr1[i] = min(arr1[i], arr1[i + 1]);
  arr1[0] = 1;
  for (int i = 1; i <= n; i++) {
    for (long long j = arr1[i], a, b = 0; j; j %= arr1[a]) {
      a = lower_bound(arr1 + 1, arr1 + n + 1, j) - arr1 - 1;
      arr2[i] =
          max(arr2[i], arr2[a] + (n - a) * (j - j % arr1[a] - arr1[a]) + b);
      b += (n - a) * (j - j % arr1[a]);
    }
  }
  cout << arr2[n];
  return 0;
}

### Prompt

Generate a Cpp solution to the following problem:

You are given a sequence of integers a1, a2, ..., an. Let <image>, and <image> for 1 ≤ i < n. Here, <image> 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

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int n;
long long arr2[200020], arr1[200020];
int main() {
  long long a, b;
  cin >> n;
  for (int i = n; i; i--) {
    long long c;
    cin >> c;
    arr1[i] = c;
  }
  for (int i = n - 1; i; i--) arr1[i] = min(arr1[i], arr1[i + 1]);
  arr1[0] = 1;
  for (int i = 1; i <= n; i++) {
    for (long long j = arr1[i], a, b = 0; j; j %= arr1[a]) {
      a = lower_bound(arr1 + 1, arr1 + n + 1, j) - arr1 - 1;
      arr2[i] =
          max(arr2[i], arr2[a] + (n - a) * (j - j % arr1[a] - arr1[a]) + b);
      b += (n - a) * (j - j % arr1[a]);
    }
  }
  cout << arr2[n];
  return 0;
}

```