#include <bits/stdc++.h>
#pragma GCC optimize("O2,Ofast,inline,unroll-all-loops,-ffast-math")
#pragma GCC target("popcnt")
using namespace std;
int n;
long long a[200010], ans = 0;
map<long long, long long> M;
template <class T>
void read(T &x) {
  char ch = x = 0;
  bool fl = false;
  while (!isdigit(ch)) fl |= ch == '-', ch = getchar();
  while (isdigit(ch)) x = x * 10 + ch - '0', ch = getchar();
  x = fl ? -x : x;
}
int main() {
  read(n);
  for (int i = 1; i <= n; i++) {
    read(a[i]);
  }
  M[1LL << 60] = 0;
  for (int i = 1; i <= n; i++) {
    for (auto it = M.lower_bound(a[i]); it != M.end(); it = M.erase(it)) {
      long long x = it->first, y = it->second;
      M[x % a[i]] = max(M[x % a[i]], y + 1LL * (i - 1) * (x - x % a[i]));
      M[a[i] - 1] =
          max(M[a[i] - 1], y + 1LL * (i - 1) * ((x + 1) / a[i] * a[i] - a[i]));
    }
  }
  for (auto it = M.begin(); it != M.end(); ++it) {
    ans = max(ans, it->second + 1LL * n * it->first);
  }
  printf("%lld\n", ans);
  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>
#pragma GCC optimize("O2,Ofast,inline,unroll-all-loops,-ffast-math")
#pragma GCC target("popcnt")
using namespace std;
int n;
long long a[200010], ans = 0;
map<long long, long long> M;
template <class T>
void read(T &x) {
  char ch = x = 0;
  bool fl = false;
  while (!isdigit(ch)) fl |= ch == '-', ch = getchar();
  while (isdigit(ch)) x = x * 10 + ch - '0', ch = getchar();
  x = fl ? -x : x;
}
int main() {
  read(n);
  for (int i = 1; i <= n; i++) {
    read(a[i]);
  }
  M[1LL << 60] = 0;
  for (int i = 1; i <= n; i++) {
    for (auto it = M.lower_bound(a[i]); it != M.end(); it = M.erase(it)) {
      long long x = it->first, y = it->second;
      M[x % a[i]] = max(M[x % a[i]], y + 1LL * (i - 1) * (x - x % a[i]));
      M[a[i] - 1] =
          max(M[a[i] - 1], y + 1LL * (i - 1) * ((x + 1) / a[i] * a[i] - a[i]));
    }
  }
  for (auto it = M.begin(); it != M.end(); ++it) {
    ans = max(ans, it->second + 1LL * n * it->first);
  }
  printf("%lld\n", ans);
  return 0;
}

```