Codeforces Round 923 (Div. 3) |
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Finished |

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constructive algorithms

greedy

strings

*900

No tag edit access

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B. Following the String

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPolycarp 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 $$$a_i$$$ is the number of such indices $$$j$$$ ($$$j < i$$$) that $$$s_i=s_j$$$. 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 $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. Then the descriptions of the test cases follow.

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

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$0 \le a_i < n$$$) — 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 $$$2 \cdot 10^5$$$.

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

5110 0 0 1 0 2 0 3 1 1 4100 0 0 0 0 1 0 1 1 01080 1 2 3 4 5 6 780 0 0 0 0 0 0 0

Output

abracadabra codeforces a aaaaaaaa dijkstra

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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