Maximum Value(CodeForces - 484B)

Maximum Value

Time limit 1000 ms

Memory limit 262144 kB

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

Input

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

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

Output

Print the answer to the problem.

Example

Input

3
3 4 5

Output

2

题意：求aj%ai的最大值，其中j>i;
分析：每次寻找小于k*aj的最大值，类似于素数筛，例如n=5时，3 4 5 6 7 ，我们如果查找对3取模的最大值，毫无疑问就是找到3到2*3中间的最大值；

AC代码：

#include<iostream>
#include<cstdio>
#include<string>
#include<cstring>
#include<algorithm>
#include<cmath>
#define N 2*100000+10
const int maxn=1000000+10;
typedef long long ll;
using namespace std;
int a[N];
int n;
int C(int x){
    int w=x,ans=0;
    while (w<a[n-1]){
       w+=x;
       int k=lower_bound(a,a+n,w)-a;
       if (k==0) continue;
       else k--;
       if (a[k]<=x) continue;
       ans=max(ans,a[k]%x);
    }
    return ans;
}
int main(){
    ios::sync_with_stdio(false);
    int ans=0;
    scanf("%d",&n);
    for (int i=0;i<n;i++)  scanf("%d",&a[i]);
    sort(a,a+n);
    for (int i=n-1;i>=0;i--){
         if (i<n-1&&a[i]==a[i+1])
          continue;
         if (ans>=a[i]-1)
           break;
         ans=max(ans,C(a[i]));
    }
   printf("%d\n",ans);
    return 0;
}