from sys import stdin
input = stdin.readline

limit = 1<<60

def func(n, C, cnt):
    if n == 0: return True
    for i in range(n, N*2+10):
        cnt += C[i]
        C[i] = 0
    SUM = 0
    for i in reversed(range(n)):
        if 1 <= i:
            C[i] -= SUM
        if C[i] <= 0:
            a = 1-C[i]
            SUM += a
            C[i] = 1
        if 2 <= C[i]:
            cnt += C[i]-1
            C[i] = 1
        if limit <= SUM: return False
    return SUM <= cnt

for _ in range(int(input())):
    N = int(input())
    A = list(map(int, input().split()))

    if N == 1:
        print(max(A[0], 1))
        continue

    C = [0]*(N*2+10)
    cnt = 0
    for a in A:
        if a < N*2+10:
            C[a] += 1
        else:
            cnt += 1

    left = 0
    right = N*2+10
    while left+1 < right:
        mid = (left+right)//2
        if func(mid, C[:], cnt):
            left = mid
        else:
            right = mid

    print(max(left, 1))