Statement

## Goal

An old safe has a dial lock with numbers 0 to 89. The dial may turn round and round in either direction. Being an old safe it will open within 3 numbers or closer in either direction to the KEY.

Your task is to determine if the safe opens or remains shut and output the opening number.

Example:
KEY 30
COMBINATION 0>80<50>100<5>14<20

`start:          0, move clockwise by 80        80, move counter clockwise by 50        30, move clockwise by 100        40, move counter clockwise by 5        35, move clockwise by 14        49, move counter clockwise by 20        29 `

|30 - 29| <= 3 so the safe will OPEN

Output:

`OPEN29`

Note: during the combination the safe stopped on the opening number but will not open as it is a safe and needs the full COMBINATION to open. Only the final result may open the safe.
Input
Line 1: KEY the number that will open the safe.
Line 2: COMBINATION A start number followed by a sequence of rotations either > clockwise by a number and/or < counter-clockwise by a number.
Output
Line 1: OPEN or LOCKED
Line 2: The opening or locked number
Constraints
0<=KEY<=89
1<=COMBINATION length<=250
rotations will be either > or <
0<=rotation number<=1000
Example
Input
```30
0>80<50>100<5>14<20```
Output
```OPEN
29```

Game modes
FastestShortest

Test cases
Test
Input
30 0>80<50>100<5>14<20
Output
OPEN 29

Validator 1 Validator
Input
20 0>50<10>135<80>13
Output
OPEN 18

Zero start Test
Input
0 0>91<89
Output
OPEN 2

Validator 2 Validator
Input
0 0<89>90
Output
OPEN 1

Test 3 Test
Input
89 20>31<30>80<15>18
Output
LOCKED 14

Validator 3 Validator
Input
88 31>40<32>45<80
Output
LOCKED 4

Test 4 Test
Input
24 89>2<100>88<2>30
Output
LOCKED 17

Validator 4 Validator
Input
33 0>2<20>40<20>40<2>16
Output
LOCKED 56

Limit Test
Input
10 89>39<29>1000<30
Output
LOCKED 79

Validator 5 Validator
Input
10 10>1000<9>1<100>8
Output
OPEN 10

One turn Test
Input
15 2<118
Output
LOCKED 64

Validator 6 Validator
Input
7 0>98
Output
OPEN 8

Uncrackable Test
Input
40 1>2>3<2<1>4>6>8>100<12<1>3<1000>99<1>999<1>1000>3<22>22
Output
OPEN 40

Validator 7 Validator
Input
70 1>2>3<2<1>4>6>8>100<12<1>3<1000>99<1>999<1>1000>3<22
Output
LOCKED 18

Around zero Test
Input
0 0<5>8<3>9<12
Output
OPEN 87

Validator 8 Validator
Input
0 0<3>5<1
Output
OPEN 1

High KEY Test
Input
88 3<20>40<22
Output
OPEN 1

Validator 9 Validator
Input
87 3<20>40<23
Output
OPEN 0

Solution language

Solution

Stub generator input
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