#include <bits/stdc++.h>
using namespace std;
map<long long, long long> st;
long long n, a[200100], lst;
int main() {
  cin >> n;
  for (int i = 1; i <= n; ++i) cin >> a[i];
  st[a[1] - 1] = 0, lst = a[1];
  for (int i = 2; i <= n; ++i)
    if (a[i] < lst) {
      for (auto it = st.lower_bound(a[i]); it != st.end(); st.erase(it++))
        st[a[i] - 1] =
            max(st[a[i] - 1],
                it->second + (i - 1) * (it->first - it->first % a[i] - a[i])),
                  st[it->first % a[i]] = max(
                      st[it->first % a[i]],
                      it->second + (i - 1) * (it->first - it->first % a[i]));
      lst = a[i];
    }
  lst = 0;
  for (auto it : st) lst = max(lst, it.first * n + it.second);
  cout << lst;
}

### 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;
map<long long, long long> st;
long long n, a[200100], lst;
int main() {
  cin >> n;
  for (int i = 1; i <= n; ++i) cin >> a[i];
  st[a[1] - 1] = 0, lst = a[1];
  for (int i = 2; i <= n; ++i)
    if (a[i] < lst) {
      for (auto it = st.lower_bound(a[i]); it != st.end(); st.erase(it++))
        st[a[i] - 1] =
            max(st[a[i] - 1],
                it->second + (i - 1) * (it->first - it->first % a[i] - a[i])),
                  st[it->first % a[i]] = max(
                      st[it->first % a[i]],
                      it->second + (i - 1) * (it->first - it->first % a[i]));
      lst = a[i];
    }
  lst = 0;
  for (auto it : st) lst = max(lst, it.first * n + it.second);
  cout << lst;
}

```