#include <bits/stdc++.h>
using namespace std;
int main() {
  int n;
  scanf("%d", &n);
  map<long long, long long> f;
  f[(long long)1e18] = 0;
  for (int i = 1; i <= n; ++i) {
    long long md;
    scanf("%lld", &md);
    for (auto it = f.lower_bound(md); it != f.end(); f.erase(it++)) {
      f[md - 1] = max(f[md - 1],
                      it->second + (it->first - it->first % md - md) * (i - 1));
      f[it->first % md] =
          max(f[it->first % md],
              it->second + (it->first - it->first % md) * (i - 1));
    }
  }
  long long ans = 0;
  for (auto it : f) {
    ans = max(ans, it.first * n + it.second);
  }
  printf("%lld\n", ans);
}

### Prompt

Your challenge is to write 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 main() {
  int n;
  scanf("%d", &n);
  map<long long, long long> f;
  f[(long long)1e18] = 0;
  for (int i = 1; i <= n; ++i) {
    long long md;
    scanf("%lld", &md);
    for (auto it = f.lower_bound(md); it != f.end(); f.erase(it++)) {
      f[md - 1] = max(f[md - 1],
                      it->second + (it->first - it->first % md - md) * (i - 1));
      f[it->first % md] =
          max(f[it->first % md],
              it->second + (it->first - it->first % md) * (i - 1));
    }
  }
  long long ans = 0;
  for (auto it : f) {
    ans = max(ans, it.first * n + it.second);
  }
  printf("%lld\n", ans);
}

```