Codeforces485D(SummerTrainingDay01-K)

D. Maximum Value

time limit per test：1 second

memory limit per test：256 megabytes

input：standard input

output：standard output

You are given a sequence a consisting of n integers. Find the maximum possible value of  (integer remainder of ai divided by aj), where 1 ≤ i, j ≤ n and ai ≥ aj.

Input

The first line contains integer n — the length of the sequence (1 ≤ n ≤ 2·105).

The second line contains n space-separated integers ai (1 ≤ ai ≤ 106).

Output

Print the answer to the problem.

Examples

input

3
3 4 5

output

2

 //2017-08-17
 #include <cstdio>
 #include <iostream>
 #include <cstring>
 #include <algorithm>

 using namespace std;

 const int N = ;
 const int M = ;
 //book[i]记录i是否出现过，pre[i]表示比i小的出现过的最大的数
 int a[N], n, book[M], pre[M];

 int main()
 {
     while (scanf("%d", &n) != EOF)
     {
         memset(book, , sizeof(book));
         for (int i = ; i < n; i++){
             scanf("%d", &a[i]);
             book[a[i]] = ;
         }
         sort(a, a + n);
         n = unique(a, a+n)-a;
         int ans = , maxinum = (a[n-]<<), ptr = ;
         for(int i = ; i <= maxinum; i++){
             pre[i] = ptr;
             if(book[i])ptr = i;
         }
         for (int i = ; i < n; i++){
             for (int j = a[i]<<; j <= maxinum; j+=a[i]){
                 ans = max(ans, a[i]-j+pre[j]);
             }
         }
         printf("%d\n", ans);
     }
     return ;
 }