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This round has an unusual addition to the rules. For each problem you must use distinct language. Thus, if you have a submission that has passed at least one test or is being tested at the moment, then for this task you can use only this language and can not use it for other tasks. More details can be read by the link. Different implementations of the same language are considered to be the same language (for example, in C++ you can only solve one problem, regardless of the exact chosen compiler).

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H. Repairing Of String

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputStepan had a favorite string *s* which consisted of the lowercase letters of the Latin alphabet.

After graduation, he decided to remember it, but it was a long time ago, so he can't now remember it. But Stepan remembers some information about the string, namely the sequence of integers *c*_{1}, *c*_{2}, ..., *c*_{n}, where *n* equals the length of the string *s*, and *c*_{i} equals the number of substrings in the string *s* with the length *i*, consisting of the same letters. The substring is a sequence of consecutive characters in the string *s*.

For example, if the Stepan's favorite string is equal to "tttesst", the sequence *c* looks like: *c* = [7, 3, 1, 0, 0, 0, 0].

Stepan asks you to help to repair his favorite string *s* according to the given sequence *c*_{1}, *c*_{2}, ..., *c*_{n}.

Input

The first line contains the integer *n* (1 ≤ *n* ≤ 2000) — the length of the Stepan's favorite string.

The second line contains the sequence of integers *c*_{1}, *c*_{2}, ..., *c*_{n} (0 ≤ *c*_{i} ≤ 2000), where *c*_{i} equals the number of substrings of the string *s* with the length *i*, consisting of the same letters.

It is guaranteed that the input data is such that the answer always exists.

Output

Print the repaired Stepan's favorite string. If there are several answers, it is allowed to print any of them. The string should contain only lowercase letters of the English alphabet.

Examples

Input

6

6 3 1 0 0 0

Output

kkrrrq

Input

4

4 0 0 0

Output

abcd

Note

In the first test Stepan's favorite string, for example, can be the string "kkrrrq", because it contains 6 substrings with the length 1, consisting of identical letters (they begin in positions 1, 2, 3, 4, 5 and 6), 3 substrings with the length 2, consisting of identical letters (they begin in positions 1, 3 and 4), and 1 substring with the length 3, consisting of identical letters (it begins in the position 3).

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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