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

题目大意
给你一个长度为n的序列，让你求aj%ai的最大值
分析
由于n是10的5次方的数，所以不能n2的循环，我们对于每一个数可以考虑他的倍数，对于ai，寻找在ai*（k-1）到ai*k
之间的最大数

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
#include <vector>
using namespace std;
const int maxn = 200000 + 10;
const int maxm= 1000000 + 10;
int a[maxn];
int vis[2*maxm];
int main()
{
    int n;
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
    {
        scanf("%d",&a[i]);
        vis[a[i]]=a[i];
    }
    vis[1]=1;
    for(int i=1;i<2*maxm;i++)
    {
        if(!vis[i]) vis[i]=vis[i-1];
    }
    int max_=0;
    for(int i=1;i<maxm;i++)
    {
        if(vis[i]==i)
        for(int j=2*i;j<2*maxm;j+=i)
        {
            if(vis[j-1]>i)
            max_=max(max_,(vis[j-1])%i);
        }
    }
    printf("%d\n",max_);
    return 0;
}