# Cypher solution codeforces

Luca has a cypher made up of a sequence of n wheels, each with a digit ai written on it. On the i-th wheel, he made bi moves. Each move is one of two types:

• up move (denoted by U): it increases the i-th digit by 11. After applying the up move on 99, it becomes 00.
• down move (denoted by D): it decreases the i-th digit by 11. After applying the down move on 00, it becomes 99.

## Cypher solution codeforces

Example for =4n=4. The current sequence is 0 0 0 0.
Luca knows the final sequence of wheels and the moves for each wheel. Help him find the original sequence and crack the cypher.

## Cypher solution codeforces

The first line contains a single integer t (11001≤t≤100) — the number of test cases.

The first line of each test case contains a single integer n (11001≤n≤100) — the number of wheels.

The second line contains n integers ai (090≤ai≤9) — the digit shown on the i-th wheel after all moves have been performed.

Then n lines follow, the i-th of which contains the integer bi (1101≤bi≤10) and bi characters that are either U or D — the number of moves performed on the i-th wheel, and the moves performed. U and D represent an up move and a down move respectively.

Output

For each test case, output n space-separated digits  — the initial sequence of the cypher.

## Cypher solution codeforces

Example
input

Copy
3
3
9 3 1
3 DDD
4 UDUU
2 DU
2
0 9
9 DDDDDDDDD
9 UUUUUUUUU
5
0 5 9 8 3
10 UUUUUUUUUU
3 UUD
8 UUDUUDDD
10 UUDUUDUDDU
4 UUUU

output

Copy
2 1 1
9 0
0 4 9 6 9


## Cypher solution codeforces

In the first test case, we can prove that initial sequence was [2,1,1][2,1,1]. In that case, the following moves were performed:

• On the first wheel: 2−→1−→0−→92→D1→D0→D9.
• On the second wheel: 1−→2−→1−→2−→31→U2→D1→U2→U3.
• On the third wheel: 1−→0−→11→D0→U1.

The final sequence was [9,3,1][9,3,1], which matches the input.