1406_A. Subset Mex
Given a set of integers (it can contain equal elements).

You have to split it into two subsets A and B (both of them can contain equal elements or be empty). You have to maximize the value of mex(A)+mex(B).

Here mex of a set denotes the smallest non-negative integer that doesn't exist in the set. For example: 

  * mex(\{1,4,0,2,2,1\})=3 
  * mex(\{3,3,2,1,3,0,0\})=4 
  * mex(∅)=0 (mex for empty set) 



The set is splitted into two subsets A and B if for any integer number x the number of occurrences of x into this set is equal to the sum of the number of occurrences of x into A and the number of occurrences of x into B.

Input

The input consists of multiple test cases. The first line contains an integer t (1≤ t≤ 100) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer n (1≤ n≤ 100) — the size of the set.

The second line of each testcase contains n integers a_1,a_2,... a_n (0≤ a_i≤ 100) — the numbers in the set.

Output

For each test case, print the maximum value of mex(A)+mex(B).

Example

Input


4
6
0 2 1 5 0 1
3
0 1 2
4
0 2 0 1
6
1 2 3 4 5 6


Output


5
3
4
0

Note

In the first test case, A=\left\{0,1,2\right\},B=\left\{0,1,5\right\} is a possible choice.

In the second test case, A=\left\{0,1,2\right\},B=∅ is a possible choice.

In the third test case, A=\left\{0,1,2\right\},B=\left\{0\right\} is a possible choice.

In the fourth test case, A=\left\{1,3,5\right\},B=\left\{2,4,6\right\} is a possible choice.
```python
t=int(input())
while t!=0:
    t-=1
    n=int(input())
    li=list(map(int,input().split()))
    dic={}
    dic2={}
    a=0
    b=0
    flag=0
    ans=[0]*101
    for i in li:
        if i not in dic and i not in dic2:
            dic[i]=1
        else:
            ans[i]=1
            dic2[i]=1
            if i in dic:
                dic.pop(i)
    le=len(dic2)
    c=0
    for i in range(0,101):
        if ans[i]==0 and le!=0:
            if c<le:
                a=i
                
                flag=1
                break
            else:
                break
        else:
            c+=1
    if flag==0:
        a=le
    for i in dic:
        ans[i]=1
    for j in range(0,101):
        if ans[j]==0:
            b=j
            
            break
    print(a+b)
        
    
                
                
        
            
            
    
    

    
        
         
        
        
            
            

```