#include <bits/stdc++.h>
using namespace std;
const int N = 200005;
int n;
long long a[N];
struct node {
  long long j, k;
  node(long long _j = 0, long long _k = 0) {
    j = _j;
    k = _k;
  }
  bool operator<(const node &y) const {
    if (j != y.j)
      return j > y.j;
    else
      return k > y.k;
  }
};
set<node> S;
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%lld", &a[i]);
  S.insert(node(a[1] - 1, 0));
  for (int i = 1; i < n; i++) {
    long long m = a[i + 1], mx = 0;
    bool Ok = 0;
    while (1) {
      set<node>::iterator it = S.begin();
      long long j = (*it).j, k = (*it).k;
      if (j < m) break;
      Ok = 1;
      mx = max(mx, k + 1ll * i * (j - j % m - m));
      S.erase(it);
      S.insert(node(j % m, k + 1ll * i * (j - j % m)));
    }
    if (Ok) S.insert(node(m - 1, mx));
  }
  long long ans = 0;
  for (set<node>::iterator it = S.begin(); it != S.end(); it++) {
    long long j = (*it).j, k = (*it).k;
    ans = max(ans, k + j * n);
  }
  printf("%lld\n", ans);
  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;
const int N = 200005;
int n;
long long a[N];
struct node {
  long long j, k;
  node(long long _j = 0, long long _k = 0) {
    j = _j;
    k = _k;
  }
  bool operator<(const node &y) const {
    if (j != y.j)
      return j > y.j;
    else
      return k > y.k;
  }
};
set<node> S;
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%lld", &a[i]);
  S.insert(node(a[1] - 1, 0));
  for (int i = 1; i < n; i++) {
    long long m = a[i + 1], mx = 0;
    bool Ok = 0;
    while (1) {
      set<node>::iterator it = S.begin();
      long long j = (*it).j, k = (*it).k;
      if (j < m) break;
      Ok = 1;
      mx = max(mx, k + 1ll * i * (j - j % m - m));
      S.erase(it);
      S.insert(node(j % m, k + 1ll * i * (j - j % m)));
    }
    if (Ok) S.insert(node(m - 1, mx));
  }
  long long ans = 0;
  for (set<node>::iterator it = S.begin(); it != S.end(); it++) {
    long long j = (*it).j, k = (*it).k;
    ans = max(ans, k + j * n);
  }
  printf("%lld\n", ans);
  return 0;
}

```