Project Euler #185: Number Mind

_{This problem is a programming version of Problem 185 from projecteuler.net}

The game Number Mind is a variant of the well known game Master Mind.

Instead of coloured pegs, you have to guess a secret sequence of digits. After each guess you're only told in how many places you've guessed the correct digit. So, if the sequence was and you guessed , you'd be told that you have one correct digit; however, you would NOT be told that you also have another digit in the wrong place.

For instance, given the following guesses for a -digit secret sequence,

; correct
; correct
; correct
; correct
; correct
; correct

The correct sequence is unique.

Based on the some guesses, find the unique -digit secret sequence.

Input Format

First line of every input file contains a single integer the number of guesses. lines follow each containing the -digit guess sequence and the number of correct digits for this guess .

Constraints

Output Format

Output the string with exactly digits the unique valid answer to the guesses.

Sample Input

20
228569150065 1
907564288621 0
496954400043 0
713459943615 0
211421327491 1
258317293172 0
919252724339 1
197103476352 0
151173430038 0
063794395936 0
504759866532 1
502906565456 0
790539816536 0
595873942664 1
346602334981 0
988808475766 1
559203789779 0
498580144863 1
441454897857 1
622818801178 0

Sample Output

884045122207