#include <bits/stdc++.h>
using namespace std;
const long double pi = acos(-1);
const int oo = 1 << 30;
const long long OO = 1e18;
const int N = 2e5 + 100;
long long gi() {
  long long w = 0;
  bool q = 1;
  char c = getchar();
  while ((c < '0' || c > '9') && c != '-') c = getchar();
  if (c == '-') q = 0, c = getchar();
  while (c >= '0' && c <= '9') w = w * 10 + c - '0', c = getchar();
  return q ? w : -w;
}
int main() {
  int n = gi(), i;
  long long x, y = gi(), ans = 0;
  map<long long, long long> s;
  s[y - 1] = 0;
  for (i = 1; i < n; i++)
    if ((x = gi()) < y)
      for (auto t = s.lower_bound(y = x); t != s.end(); s.erase(t++)) {
        s[x - 1] = max(s[x - 1], t->second + (t->first - x + 1) / x * x * i);
        s[t->first % x] =
            max(s[t->first % x], t->second + t->first / x * x * i);
      }
  for (auto t : s) ans = max(ans, t.first * n + t.second);
  cout << ans << endl;
  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 long double pi = acos(-1);
const int oo = 1 << 30;
const long long OO = 1e18;
const int N = 2e5 + 100;
long long gi() {
  long long w = 0;
  bool q = 1;
  char c = getchar();
  while ((c < '0' || c > '9') && c != '-') c = getchar();
  if (c == '-') q = 0, c = getchar();
  while (c >= '0' && c <= '9') w = w * 10 + c - '0', c = getchar();
  return q ? w : -w;
}
int main() {
  int n = gi(), i;
  long long x, y = gi(), ans = 0;
  map<long long, long long> s;
  s[y - 1] = 0;
  for (i = 1; i < n; i++)
    if ((x = gi()) < y)
      for (auto t = s.lower_bound(y = x); t != s.end(); s.erase(t++)) {
        s[x - 1] = max(s[x - 1], t->second + (t->first - x + 1) / x * x * i);
        s[t->first % x] =
            max(s[t->first % x], t->second + t->first / x * x * i);
      }
  for (auto t : s) ans = max(ans, t.first * n + t.second);
  cout << ans << endl;
  return 0;
}

```