#include <bits/stdc++.h>
using namespace std;
set<pair<long long, long long> > S;
set<pair<long long, long long> >::iterator it;
int n;
long long a[200005], ans;
pair<long long, long long> u;
void ins(pair<long long, long long> o) {
  it = S.upper_bound(pair<long long, long long>(o.first, -100));
  if (it != S.end() && it->first == o.first) {
    if (it->second < o.second) S.erase(it), S.insert(o);
  } else
    S.insert(o);
}
int main() {
  int i;
  scanf("%d", &n);
  for (i = 1; i <= n; i++) scanf("%I64d", &a[i]);
  S.insert(pair<long long, long long>(a[1], 0));
  for (i = 2; i <= n; i++) {
    while (S.size()) {
      it = S.end(), it--;
      if (it->first <= a[i]) break;
      u = (*it), S.erase(it);
      ins(pair<long long, long long>(
          a[i], u.second + (u.first / a[i] - 1) * (i - 1) * a[i]));
      if (u.first % a[i] != 0)
        ins(pair<long long, long long>(
            u.first % a[i], (u.first / a[i]) * (i - 1) * a[i] + u.second));
    }
  }
  while (S.size()) {
    it = S.begin();
    ans = max(ans, it->second + (it->first - 1) * n);
    S.erase(it);
  }
  cout << ans;
  return 0;
}

### Prompt

Please create a solution in CPP 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;
set<pair<long long, long long> > S;
set<pair<long long, long long> >::iterator it;
int n;
long long a[200005], ans;
pair<long long, long long> u;
void ins(pair<long long, long long> o) {
  it = S.upper_bound(pair<long long, long long>(o.first, -100));
  if (it != S.end() && it->first == o.first) {
    if (it->second < o.second) S.erase(it), S.insert(o);
  } else
    S.insert(o);
}
int main() {
  int i;
  scanf("%d", &n);
  for (i = 1; i <= n; i++) scanf("%I64d", &a[i]);
  S.insert(pair<long long, long long>(a[1], 0));
  for (i = 2; i <= n; i++) {
    while (S.size()) {
      it = S.end(), it--;
      if (it->first <= a[i]) break;
      u = (*it), S.erase(it);
      ins(pair<long long, long long>(
          a[i], u.second + (u.first / a[i] - 1) * (i - 1) * a[i]));
      if (u.first % a[i] != 0)
        ins(pair<long long, long long>(
            u.first % a[i], (u.first / a[i]) * (i - 1) * a[i] + u.second));
    }
  }
  while (S.size()) {
    it = S.begin();
    ans = max(ans, it->second + (it->first - 1) * n);
    S.erase(it);
  }
  cout << ans;
  return 0;
}

```