13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T764,

Given an array $$$a$$$, let $$$f(x)$$$ be the number of occurrences of $$$x$$$ in the array $$$a$$$. For example, when $$$a=[1,2,3,1,4]$$$, then $$$f(1)=2$$$ and $$$f(3)=1$$$.

You have an array $$$b$$$ of size $$$n$$$. Please determine if there is an array $$$a$$$ of size $$$n$$$ such that $$$f(a_i)=b_i$$$ for all $$$1 \leq i \leq n$$$. If there is one, construct it.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ ($$$1 \leq n \leq 2\cdot 10^5$$$).

The second line contains $$$n$$$ integers $$$b_1,b_2,\ldots,b_n$$$ ($$$1 \leq b_i \leq n$$$).

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

Output

For each test case, output $$$-1$$$ if there is no valid

Replace with Occurrences

Examples