#include <bits/stdc++.h>
using namespace std;
inline long long Getint() {
  char ch = getchar();
  long long x = 0, fh = 1;
  while (ch < '0' || ch > '9') {
    if (ch == '-') fh = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    (x *= 10) += ch ^ 48;
    ch = getchar();
  }
  return x * fh;
}
const int N = 200005;
int n;
long long A[N];
map<long long, long long> f;
map<long long, long long>::iterator it;
inline bool Chkmax(long long &x, long long y) { return x < y ? x = y, 1 : 0; }
int main() {
  n = Getint();
  for (int i = 1; i <= n; i++) A[i] = Getint();
  f[A[1] - 1] = 0;
  for (int i = 2; i <= n; i++) {
    while (f.end() != f.begin()) {
      it = f.end();
      it--;
      long long r = it->first, k = it->second;
      if (r < A[i]) break;
      f.erase(it);
      if (f.find(r % A[i]) == f.end()) f[r % A[i]] = 0;
      if (f.find(A[i] - 1) == f.end()) f[A[i] - 1] = 0;
      Chkmax(f[r % A[i]], k + (r - r % A[i]) * (i - 1));
      Chkmax(f[A[i] - 1], k + (r - r % A[i] - A[i]) * (i - 1));
    }
  }
  long long Ans = 0;
  for (it = f.begin(); it != f.end(); it++) {
    long long r = it->first, k = it->second;
    Chkmax(Ans, k + r * n);
  }
  cout << Ans << '\n';
  return 0;
}

### Prompt

Develop a solution in CPP to the problem described below:

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;
inline long long Getint() {
  char ch = getchar();
  long long x = 0, fh = 1;
  while (ch < '0' || ch > '9') {
    if (ch == '-') fh = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    (x *= 10) += ch ^ 48;
    ch = getchar();
  }
  return x * fh;
}
const int N = 200005;
int n;
long long A[N];
map<long long, long long> f;
map<long long, long long>::iterator it;
inline bool Chkmax(long long &x, long long y) { return x < y ? x = y, 1 : 0; }
int main() {
  n = Getint();
  for (int i = 1; i <= n; i++) A[i] = Getint();
  f[A[1] - 1] = 0;
  for (int i = 2; i <= n; i++) {
    while (f.end() != f.begin()) {
      it = f.end();
      it--;
      long long r = it->first, k = it->second;
      if (r < A[i]) break;
      f.erase(it);
      if (f.find(r % A[i]) == f.end()) f[r % A[i]] = 0;
      if (f.find(A[i] - 1) == f.end()) f[A[i] - 1] = 0;
      Chkmax(f[r % A[i]], k + (r - r % A[i]) * (i - 1));
      Chkmax(f[A[i] - 1], k + (r - r % A[i] - A[i]) * (i - 1));
    }
  }
  long long Ans = 0;
  for (it = f.begin(); it != f.end(); it++) {
    long long r = it->first, k = it->second;
    Chkmax(Ans, k + r * n);
  }
  cout << Ans << '\n';
  return 0;
}

```