#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 10;
inline void Read(long long &x) {
  x = 0;
  register char cc = '\0';
  int fff = 1;
  for (; cc < '0' || cc > '9'; cc = getchar())
    if (cc == '-') fff = -1;
  for (; cc >= '0' && cc <= '9'; cc = getchar())
    x = (x << 1) + (x << 3) + (cc & 15);
  x *= fff;
}
map<long long, long long> mp;
long long n, tot, fans, a[N], nxtj[N << 1], nxtf[N << 1];
int main() {
  Read(n);
  for (int i = 1; i <= n; ++i) Read(a[i]);
  mp[a[1] - 1] = 0;
  for (int i = 2; i <= n; ++i) {
    long long nowm = a[i];
    tot = 0;
    map<long long, long long>::iterator it = mp.lower_bound(nowm);
    for (map<long long, long long>::iterator j = it; j != mp.end(); ++j) {
      nxtj[++tot] = (j->first) % nowm;
      nxtf[tot] = (j->second) + (i - 1) * ((j->first) - (j->first) % nowm);
      nxtj[++tot] = nowm - 1;
      nxtf[tot] =
          (j->second) + (i - 1) * (((j->first) + 1) / nowm * nowm - nowm);
    }
    mp.erase(it, mp.end());
    for (register int j = 1; j <= tot; ++j)
      mp[nxtj[j]] = max(mp[nxtj[j]], nxtf[j]);
  }
  for (map<long long, long long>::iterator it = mp.begin(); it != mp.end();
       ++it)
    fans = max(fans, it->second + (it->first) * n);
  cout << fans << endl;
  return 0;
}

### Prompt

Create a solution in cpp for 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 int N = 2e5 + 10;
inline void Read(long long &x) {
  x = 0;
  register char cc = '\0';
  int fff = 1;
  for (; cc < '0' || cc > '9'; cc = getchar())
    if (cc == '-') fff = -1;
  for (; cc >= '0' && cc <= '9'; cc = getchar())
    x = (x << 1) + (x << 3) + (cc & 15);
  x *= fff;
}
map<long long, long long> mp;
long long n, tot, fans, a[N], nxtj[N << 1], nxtf[N << 1];
int main() {
  Read(n);
  for (int i = 1; i <= n; ++i) Read(a[i]);
  mp[a[1] - 1] = 0;
  for (int i = 2; i <= n; ++i) {
    long long nowm = a[i];
    tot = 0;
    map<long long, long long>::iterator it = mp.lower_bound(nowm);
    for (map<long long, long long>::iterator j = it; j != mp.end(); ++j) {
      nxtj[++tot] = (j->first) % nowm;
      nxtf[tot] = (j->second) + (i - 1) * ((j->first) - (j->first) % nowm);
      nxtj[++tot] = nowm - 1;
      nxtf[tot] =
          (j->second) + (i - 1) * (((j->first) + 1) / nowm * nowm - nowm);
    }
    mp.erase(it, mp.end());
    for (register int j = 1; j <= tot; ++j)
      mp[nxtj[j]] = max(mp[nxtj[j]], nxtf[j]);
  }
  for (map<long long, long long>::iterator it = mp.begin(); it != mp.end();
       ++it)
    fans = max(fans, it->second + (it->first) * n);
  cout << fans << endl;
  return 0;
}

```