#include <bits/stdc++.h>
using namespace std;
long long n, x, y, sl, ans, a[200010];
map<long long, long long> dp;
char gc() {
  return getchar();
  static char buf[1 << 16], *S, *T;
  if (S == T) {
    T = (S = buf) + fread(buf, 1, 1 << 16, stdin);
    if (S == T) return EOF;
  }
  return *S++;
}
long long rd() {
  sl = 0;
  char ch = gc();
  while (ch < '0' || '9' < ch) ch = gc();
  while ('0' <= ch && ch <= '9') sl = sl * 10 + ch - '0', ch = gc();
  return sl;
}
int main() {
  n = rd();
  for (int i = 1; i <= n; ++i) a[i] = rd();
  dp[a[1] - 1] = 0;
  for (int i = 1; i < n; ++i)
    for (map<long long, long long>::iterator j = dp.lower_bound(a[i + 1]);
         j != dp.end(); dp.erase(j++)) {
      x = j->first;
      y = j->second;
      dp[x % a[i + 1]] = max(dp[x % a[i + 1]], y + i * (x - x % a[i + 1]));
      dp[a[i + 1] - 1] = max(
          dp[a[i + 1] - 1], y + i * ((x + 1) / a[i + 1] * a[i + 1] - a[i + 1]));
    }
  for (map<long long, long long>::iterator i = dp.begin(); i != dp.end(); ++i) {
    x = i->first;
    y = i->second;
    ans = max(ans, x * n + y);
  }
  printf("%lld\n", ans);
  return 0;
}

### Prompt

Please create a solution in Cpp to 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;
long long n, x, y, sl, ans, a[200010];
map<long long, long long> dp;
char gc() {
  return getchar();
  static char buf[1 << 16], *S, *T;
  if (S == T) {
    T = (S = buf) + fread(buf, 1, 1 << 16, stdin);
    if (S == T) return EOF;
  }
  return *S++;
}
long long rd() {
  sl = 0;
  char ch = gc();
  while (ch < '0' || '9' < ch) ch = gc();
  while ('0' <= ch && ch <= '9') sl = sl * 10 + ch - '0', ch = gc();
  return sl;
}
int main() {
  n = rd();
  for (int i = 1; i <= n; ++i) a[i] = rd();
  dp[a[1] - 1] = 0;
  for (int i = 1; i < n; ++i)
    for (map<long long, long long>::iterator j = dp.lower_bound(a[i + 1]);
         j != dp.end(); dp.erase(j++)) {
      x = j->first;
      y = j->second;
      dp[x % a[i + 1]] = max(dp[x % a[i + 1]], y + i * (x - x % a[i + 1]));
      dp[a[i + 1] - 1] = max(
          dp[a[i + 1] - 1], y + i * ((x + 1) / a[i + 1] * a[i + 1] - a[i + 1]));
    }
  for (map<long long, long long>::iterator i = dp.begin(); i != dp.end(); ++i) {
    x = i->first;
    y = i->second;
    ans = max(ans, x * n + y);
  }
  printf("%lld\n", ans);
  return 0;
}

```