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A. Common Prefixes

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe length of the longest common prefix of two strings $$$s = s_1 s_2 \ldots s_n$$$ and $$$t = t_1 t_2 \ldots t_m$$$ is defined as the maximum integer $$$k$$$ ($$$0 \le k \le min(n,m)$$$) such that $$$s_1 s_2 \ldots s_k$$$ equals $$$t_1 t_2 \ldots t_k$$$.

Koa the Koala initially has $$$n+1$$$ strings $$$s_1, s_2, \dots, s_{n+1}$$$.

For each $$$i$$$ ($$$1 \le i \le n$$$) she calculated $$$a_i$$$ — the length of the longest common prefix of $$$s_i$$$ and $$$s_{i+1}$$$.

Several days later Koa found these numbers, but she couldn't remember the strings.

So Koa would like to find some strings $$$s_1, s_2, \dots, s_{n+1}$$$ which would have generated numbers $$$a_1, a_2, \dots, a_n$$$. Can you help her?

If there are many answers print any. We can show that answer always exists for the given constraints.

Input

Each test contains multiple test cases. The first line contains $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases. Description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 100$$$) — the number of elements in the list $$$a$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 50$$$) — the elements of $$$a$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$100$$$.

Output

For each test case:

Output $$$n+1$$$ lines. In the $$$i$$$-th line print string $$$s_i$$$ ($$$1 \le |s_i| \le 200$$$), consisting of lowercase Latin letters. Length of the longest common prefix of strings $$$s_i$$$ and $$$s_{i+1}$$$ has to be equal to $$$a_i$$$.

If there are many answers print any. We can show that answer always exists for the given constraints.

Example

Input

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

Output

aeren ari arousal around ari monogon monogamy monthly kevinvu kuroni kurioni korone anton loves adhoc problems

Note

In the $$$1$$$-st test case one of the possible answers is $$$s = [aeren, ari, arousal, around, ari]$$$.

Lengths of longest common prefixes are:

- Between $$$\color{red}{a}eren$$$ and $$$\color{red}{a}ri$$$ $$$\rightarrow 1$$$
- Between $$$\color{red}{ar}i$$$ and $$$\color{red}{ar}ousal$$$ $$$\rightarrow 2$$$
- Between $$$\color{red}{arou}sal$$$ and $$$\color{red}{arou}nd$$$ $$$\rightarrow 4$$$
- Between $$$\color{red}{ar}ound$$$ and $$$\color{red}{ar}i$$$ $$$\rightarrow 2$$$

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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