Educational Codeforces Round 69 (Rated for Div. 2) A - DIY Wooden Ladder

Educational Codeforces Round 69 (Rated for Div. 2)

 

A - DIY Wooden Ladder

Let's denote a k-step ladder as the following structure: exactly k+2 wooden planks, of which

• two planks of length at least k+1 — the base of the ladder;
• k planks of length at least 1 — the steps of the ladder;

Note that neither the base planks, nor the steps planks are required to be equal.

For example, ladders 1 and 3 are correct 2-step ladders and ladder 2 is a correct 1-step ladder. On the first picture the lengths of planks are [3,3] for the base and [1] for the step. On the second picture lengths are [3,3] for the base and [2] for the step. On the third picture lengths are [3,4] for the base and [2,3] for the steps.

 

 

You have n planks. The length of the i-th planks is ai. You don't have a saw, so you can't cut the planks you have. Though you have a hammer and nails, so you can assemble the improvised "ladder" from the planks.

The question is: what is the maximum number k such that you can choose some subset of the given planks and assemble a k-step ladder using them?

Input

The first line contains a single integer T (1≤T≤100) — the number of queries. The queries are independent.

Each query consists of two lines. The first line contains a single integer n (2≤n≤105) — the number of planks you have.

The second line contains n integers a1,a2,…,an (1≤ai≤105) — the lengths of the corresponding planks.

It's guaranteed that the total number of planks from all queries doesn't exceed 105.

Output

Print T integers — one per query. The i-th integer is the maximum number k, such that you can choose some subset of the planks given in the i-th query and assemble a k-step ladder using them.

Print 0 if you can't make even 1-step ladder from the given set of planks.

Example

input

4

4

1 3 1 3

3

3 3 2

5

2 3 3 4 2

3

1 1 2

output

2

1

2

0

Note

Examples for the queries 1−3 are shown at the image in the legend section.

The Russian meme to express the quality of the ladders:

 

 

题意：题目意思就是 定义k阶梯子为两边各一块木板长度至少k+1，中间k块木板至少为1 。

         问 给你n块木板，最多能搭成几阶的梯子。

思路：显然对n块木板排序之后，取最长的两块木板搭旁边的两块梯子为最优解，

　　然后就是比较 最长的这两块木板的小的这块长度-1 和 剩余木板数量 的极小值为答案。

 

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
#include<map>
#include<set>
#include<vector>
#include<queue>
using namespace std;
#define ll long long 
const int mod=1e9+7;
const int inf=1e9+7;

const int maxn=1e5+5;
int num[maxn];

int main()
{
    ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
    
    int T;
    cin>>T;
    int n;
    while(T--)
    {
        cin>>n;
        
        for(int i=0;i<n;i++)
            cin>>num[i];
        
        sort(num,num+n);
        
        cout<<min(n-2,num[n-2]-1)<<endl;        
    }
    
    return 0;
}