# B. Following the String

[Codeforces.com](https://codeforces.com/contest/1927/problem/B)

Polycarp lost the string s of length n consisting of lowercase Latin letters, but he still has its trace.

The trace of the string s
is an array a of n integers, where ai is the number of such indices j (j<i) that si=sj. For example, the trace of the string abracadabra is the array `[0,0,0,1,0,2,0,3,1,1,4]`.

Given a trace of a string, find any string s from which it could have been obtained. The string s should consist only of lowercase Latin letters a-z.


## Input

The first line of the input contains a single integer t
(1 ≤ t ≤ 10^4) — the number of test cases. Then the descriptions of the test cases follow.

The first line of each test case contains a single integer n
(1 ≤ n ≤ 2*10^5) — the length of the lost string.

The second line of each test case contains n
integers a1,a2,…,an (0 ≤ ai < n) — the trace of the string. It is guaranteed that for the given trace, there exists a suitable string s.

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


## Output

For each test case, output a string s
that corresponds to the given trace. If there are multiple such strings s, then output any of them.

The string s should consist of lowercase Latin letters a-z.

It is guaranteed that for each test case, a valid answer exists.


## Example

Input
```
5
11
0 0 0 1 0 2 0 3 1 1 4
10
0 0 0 0 0 1 0 1 1 0
1
0
8
0 1 2 3 4 5 6 7
8
0 0 0 0 0 0 0 0
```

Output
```
abracadabra
codeforces
a
aaaaaaaa
dijkstra
```