Problem: A permutation is a sequence of n integers from 1 to n, in which all numbers occur exactly once. For example, [1], [3, 5, 2, 1, 4], [1, 3, 2] are permutations, and [2, 3, 2], [4, 3, 1], [0] are not.

Polycarp was presented with a permutation p of numbers from 1 to n. However, when Polycarp came home, he noticed that in his pocket, the permutation p had turned into an array q according to the following rule: 

  * q_i = max(p_1, p_2, …, p_i). 



Now Polycarp wondered what lexicographically minimal and lexicographically maximal permutations could be presented to him.

An array a of length n is lexicographically smaller than an array b of length n if there is an index i (1 ≤ i ≤ n) such that the first i-1 elements of arrays a and b are the same, and the i-th element of the array a is less than the i-th element of the array b. For example, the array a=[1, 3, 2, 3] is lexicographically smaller than the array b=[1, 3, 4, 2].

For example, if n=7 and p=[3, 2, 4, 1, 7, 5, 6], then q=[3, 3, 4, 4, 7, 7, 7] and the following permutations could have been as p initially: 

  * [3, 1, 4, 2, 7, 5, 6] (lexicographically minimal permutation); 
  * [3, 1, 4, 2, 7, 6, 5]; 
  * [3, 2, 4, 1, 7, 5, 6]; 
  * [3, 2, 4, 1, 7, 6, 5] (lexicographically maximum permutation). 



For a given array q, find the lexicographically minimal and lexicographically maximal permutations that could have been originally presented to Polycarp.

Input

The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.

The first line of each test case contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5).

The second line of each test case contains n integers q_1, q_2, …, q_n (1 ≤ q_i ≤ n).

It is guaranteed that the array q was obtained by applying the rule from the statement to some permutation p.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case, output two lines: 

  * on the first line output n integers — lexicographically minimal permutation that could have been originally presented to Polycarp; 
  * on the second line print n integers — lexicographically maximal permutation that could have been originally presented to Polycarp; 

Example

Input


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


Output


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

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

#define DeltaCube23 ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
#define pb push_back
#define mp make_pair
#define minimum(a) *min_element(a.begin(), a.end())
#define maximum(a) *max_element(a.begin(), a.end())
#define MOD 998244353
#define forf(i,a,b) for(int i = (a); i < (b); i++)
#define forr(i,a,b) for(int i = (a); i >= (b); i--)

typedef long long int lli;
lli binpow(lli a,lli b,lli m){lli res=1;for(b%=m-1,a%=m;b>0;b>>=1,a=a*a%m)if(b&1)res=res*a%m;return res;}
lli gcd(lli a, lli b) {return b? gcd(b, a%b) : a;}

#define int lli //CAREFUL
using namespace std;

const int mx=5e3+5;    

signed main()
{
    DeltaCube23
    int t=1; 
    cin>>t;
    
    while(t--)
    {
        int n;
        cin>>n;
        vector<int> a(n+1), b(n+1);
        forf(i,0,n)
        {
			cin>>a[i];
			b[a[i]] = 1;
		}
		int num = 0;
		forf(i,0,n+1)
		{
			if(b[i] == 1)
				num++;
		}
		int num2 = n - num;
		vector<int> c(num2);
		int j = 0;
		forf(i, 1, n+1)
		{
			if(b[i] == 0)
			{
				c[j] = i;
				j++;
			} 
		}
		j = 0;
		cout<<a[0]<<" ";
		forf(i,1,n)
		{
			if(a[i] == a[i-1])
			{
				cout<<c[j]<<" ";
				j++;
			}
			else
				cout<<a[i]<<" ";
		}
		cout<<"\n";
		
		stack<int> st;
		cout<<a[0]<<" ";
		int prev = a[0];
		forf(v, 1, prev)
			st.push(v);
			
		forf(i,1,n)
		{
			if(a[i] == a[i-1])
			{
				cout<<st.top()<<" ";
				st.pop();
			}
			else
			{
				forf(v, prev+1, a[i])
					st.push(v);
				cout<<a[i]<<" ";
				prev = a[i];
			}
		}
		cout<<"\n";
    }
    return 0;
}