#include <bits/stdc++.h>
using namespace std;
const int Maxn = 200005;
long long v[Maxn], ans;
map<long long, long long> f;
int main() {
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> v[i];
  f[v[1] - 1] = 0;
  for (int i = 2; i <= n; i++) {
    while (prev(f.end())->first >= v[i]) {
      long long a, b;
      tie(a, b) = *prev(f.end());
      f[v[i] - 1] = max(f[v[i] - 1], b + (i - 1) * (a - a % v[i] - v[i]));
      f[a % v[i]] = max(f[a % v[i]], b + (i - 1) * (a - a % v[i]));
      f.erase(prev(f.end()));
    }
  }
  for (auto i : f) ans = max(ans, n * i.first + i.second);
  cout << ans << "\n";
  return 0;
}

### Prompt

In cpp, your task is to solve 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;
const int Maxn = 200005;
long long v[Maxn], ans;
map<long long, long long> f;
int main() {
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> v[i];
  f[v[1] - 1] = 0;
  for (int i = 2; i <= n; i++) {
    while (prev(f.end())->first >= v[i]) {
      long long a, b;
      tie(a, b) = *prev(f.end());
      f[v[i] - 1] = max(f[v[i] - 1], b + (i - 1) * (a - a % v[i] - v[i]));
      f[a % v[i]] = max(f[a % v[i]], b + (i - 1) * (a - a % v[i]));
      f.erase(prev(f.end()));
    }
  }
  for (auto i : f) ans = max(ans, n * i.first + i.second);
  cout << ans << "\n";
  return 0;
}

```