NPC-Bonanza (maybe)

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2017-10-12 17:12 CEST

NPC-Bonanza (maybe)

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2017-10-19 17:12 CEST
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Problem I
Copying DNA

Evolution is a seemingly random process which works in a way which resembles certain approaches we use to get approximate solutions to hard combinatorial problems. You are now to do something completely different.

Given a DNA string $S$ from the alphabet {A,C,G,T}, find the minimal number of copy operations needed to create another string $T$. You may reverse the strings you copy, and copy both from $S$ and the pieces of your partial $T$. You may put these pieces together at any time. You may only copy contiguous parts of your partial $T$, and all copied strings must be used in your final $T$. Example: From $S$ = “ACTG” create $T$ = “GTACAATTAAT

  1. Get GT......... by copying and reversing “TG” from $S$.

  2. Get GTAC....... by copying “AC” from $S$.

  3. Get GTAC...TA.. by copying “TA” from the partial $T$.

  4. Get GTAC...TAAT by copying and reversing “TA” from the partial $T$.

  5. Get GTACAATTAAT by copying “AAT” from the partial $T$.

Input

The first line of input gives a single integer, $1 \leq t \leq 100$, the number of test cases. Then follow, for each test case, a line with the string $S$ of length $1 \leq m \leq 18$, and a line with the string $T$ of length $1 \leq n \leq 18$.

Output

Output for each test case the number of copy operations needed to create $T$ from $S$, or “impossible” if it cannot be done.

Sample Input 1 Sample Output 1
5
ACGT
GTAC
A
C
ACGT
TGCA
ACGT
TCGATCGA
A
AAAAAAAAAAAAAAAAAA
2
impossible
1
4
6