Bogosort

You are given an array $$$a_1, a_2, \dots , a_n$$$. Array is good if for each pair of indexes $$$i < j$$$ the condition $$$j – a_j \ne i – a_i$$$ holds. Can you shuffle this array so that it becomes good? To shuffle an array means to reorder its elements arbitrarily (leaving the initial order is also an option).

For example, if $$$a = [1, 1, 3, 5]$$$, then shuffled arrays $$$[1, 3, 5, 1]$$$, $$$[3, 5, 1, 1]$$$ and $$$[5, 3, 1, 1]$$$ are good, but shuffled arrays $$$[3, 1, 5, 1]$$$, $$$[1, 1, 3, 5]$$$ and $$$[1, 1, 5, 3]$$$ aren’t.

It’s guaranteed that it’s always possible to shuffle an array to meet this condition.

Input

The first line contains one integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases.

The first line of each test case contains one integer $$$n$$$ ($$$1 \le n \le 100$$$) — the length of array $$$a$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \dots , a_n$$$ ($$$1 \le a_i \le 100$$$).

Output

For each test case print the shuffled version of the array $$$a$$$ which is good.

Example

input

3
1
7
4
1 1 3 5
6
3 2 1 5 6 4

output

7
1 5 1 3
2 4 6 1 3 5

Solution:

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#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
typedef vector<int> VI;
typedef long long ll;
typedef pair<int,int> PII;
typedef double db;
mt19937 mrand(random_device{}());
const ll mod=1000000007;
int rnd(int x) { return mrand() % x;}
ll powmod(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}
// head
 
int _,n,a[1010];
int main() {
    for (scanf("%d",&_);_;_--) {
        scanf("%d",&n);
        rep(i,0,n) scanf("%d",a+i);
        sort(a,a+n);
        rep(i,0,n) printf("%d%c",a[n-1-i]," \n"[i==n-1]);
    }
}

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