Description

A factory has a 3x3 inspection station array. Inspector A (red sticker) starts first, then Inspector B (blue sticker) alternates. Completing all 3 in a line (row/column/diagonal) means 'Line Inspection Complete'. However, if both inspectors complete lines simultaneously, the record is invalid (impossible since they alternate). Determine if the given inspection record is a valid completion state.

Input

Output

Constraints

• •Input is a string of length 9 (containing only A, B, .)
• •Inspector A always starts first
• •If both inspectors complete lines simultaneously, it's invalid (impossible since they alternate)

Examples

AAABB....

valid

ABAABABBA

invalid

ABABABABA

valid