#D10561. Common Prefixes
Common Prefixes
Common Prefixes
The length of the longest common prefix of two strings s = s_1 s_2 … s_n and t = t_1 t_2 … t_m is defined as the maximum integer k (0 ≤ k ≤ min(n,m)) such that s_1 s_2 … s_k equals t_1 t_2 … t_k.
Koa the Koala initially has n+1 strings s_1, s_2, ..., s_{n+1}.
For each i (1 ≤ i ≤ 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, ..., s_{n+1} which would have generated numbers a_1, a_2, ..., 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 ≤ t ≤ 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 ≤ n ≤ 100) — the number of elements in the list a.
The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 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 ≤ |s_i| ≤ 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 → 1
- Between \color{red}{ar}i and \color{red}{ar}ousal → 2
- Between \color{red}{arou}sal and \color{red}{arou}nd → 4
- Between \color{red}{ar}ound and \color{red}{ar}i → 2
inputFormat
Input
Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 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 ≤ n ≤ 100) — the number of elements in the list a.
The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 50) — the elements of a.
It is guaranteed that the sum of n over all test cases does not exceed 100.
outputFormat
Output
For each test case:
Output n+1 lines. In the i-th line print string s_i (1 ≤ |s_i| ≤ 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 → 1
- Between \color{red}{ar}i and \color{red}{ar}ousal → 2
- Between \color{red}{arou}sal and \color{red}{arou}nd → 4
- Between \color{red}{ar}ound and \color{red}{ar}i → 2
样例
4
4
1 2 4 2
2
5 3
3
1 3 1
3
0 0 0
aaaaa
abaaa
abbaa
abbab
abaab
aaaaaa
aaaaab
aaabab
aaaa
abaa
abab
aaab
a
b
a
b