LogiQuest

429. Missing Ranges

EasyArray

All numbers lie in [lower, upper] and are sorted and distinct. Print the missing ranges in the same format as Summary Ranges, or NONE.

Input format

Line 1: n lower upper Line 2: n integers (may be empty)

Output format

The missing ranges or NONE.

Example 1

Input

5 0 99
0 1 3 50 75

Output

2 4->49 51->74 76->99

Example 2

Input

0 1 1

Output

1

Constraints

0 ≤ n ≤ 10⁴

Read input from standard input and print the answer to standard output. Your code is judged against 4 test cases, most of them hidden.

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