Description

For this question, your program is required to process an input string containing only ASCII characters between ‘0’ and ‘9’, or between ‘a’ and ‘z’ (including ‘0’, ‘9’, ‘a’, ‘z’).

Your program should reorder and split all input string characters into multiple segments, and output all segments as one concatenated string. The following requirements should also be met,

1. Characters in each segment should be in strictly increasing order. For ordering, ‘9’ is larger than ‘0’, ‘a’ is larger than ‘9’, and ‘z’ is larger than ‘a’ (basically following ASCII character order).

2. Characters in the second segment must be the same as or a subset of the first segment; and every following segment must be the same as or a subset of its previous segment.

Your program should output string “” when the input contains any invalid characters (i.e., outside the ’0′-’9′ and ‘a’-’z’ range).

Input

Input consists of multiple cases, one case per line. Each case is one string consisting of ASCII characters.

Output

For each case, print exactly one line with the reordered string based on the criteria above.

样例输入

aabbccdd

007799aabbccddeeff113355zz

1234.89898

abcdefabcdefabcdefaaaaaaaaaaaaaabbbbbbbddddddee

样例输出

abcdabcd

013579abcdefz013579abcdefz

abcdefabcdefabcdefabdeabdeabdabdabdabdabaaaaaaa

Description

Consider a string set that each of them consists of {0, 1} only. All strings in the set have the same number of 0s and 1s. Write a program to find and output the K-th string according to the dictionary order. If such a string doesn’t exist, or the input is not valid, please output “Impossible”. For example, if we have two ‘0’s and two ‘1’s, we will have a set with 6 different strings, {0011, 0101, 0110, 1001, 1010, 1100}, and the 4th string is 1001.

Input

The first line of the input file contains a single integer t (1 ≤ t ≤ 10000), the number of test cases, followed by the input data for each test case.

Each test case is 3 integers separated by blank space: N, M(2 <= N + M <= 33 and N , M >= 0), K(1 <= K <= 1000000000). N stands for the number of ‘0’s, M stands for the number of ‘1’s, and K stands for the K-th of string in the set that needs to be printed as output.

Output

For each case, print exactly one line. If the string exists, please print it, otherwise print “Impossible”.

样例输入

3

2 2 2

2 2 7

4 7 47

样例输出

0101

Impossible

01010111011

Description

Find a pair in an integer array that swapping them would maximally decrease the inversion count of the array. If such a pair exists, return the new inversion count; otherwise returns the original inversion count.

Definition of Inversion: Let (A[0], A[1] … A[n]) be a sequence of n numbers. If i < j and A[i] > A[j], then the pair (i, j) is called inversion of A.

Example:

Count(Inversion({3, 1, 2})) = Count({3, 1}, {3, 2}) = 2

InversionCountOfSwap({3, 1, 2})=>

{

InversionCount({1, 3, 2}) = 1 <– swapping 1 with 3, decreases inversion count by 1

InversionCount({2, 1, 3}) = 1 <– swapping 2 with 3, decreases inversion count by 1

InversionCount({3, 2, 1}) = 3 <– swapping 1 with 2 , increases inversion count by 1

}

Input

Input consists of multiple cases, one case per line.Each case consists of a sequence of integers separated by comma.

Output

For each case, print exactly one line with the new inversion count or the original inversion count if it cannot be reduced.

样例输入

3,1,2

1,2,3,4,5

样例输出

1

0

Description

In a running system, there are many logs produced within a short period of time, we’d like to know the count of the most frequent logs.

Logs are produced by a few non-empty format strings, the number of logs is N(1=N=20000), the maximum length of each log is 256.

Here we consider a log same with another when their edit distance (see note) is = 5.

Also we have a) logs are all the same with each other produced by a certain format string b) format strings have edit distance 5 of each other.