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CSU 2055: Wells‘s Lottery

Description

As is known to all, Wells is impoverished. 
When God heard that, God decide to help the poor Wells from terrible condition.
One day Wells met God in dream, God gave Wells a secret number which will bought Wells a great fortune and gifted Wells an ablility of transforming two lottery tickets x, y into a lottery ticket z (meet the condition that z==x or y).

Wells realized that the number must be the result of lottery, which would be worth ¥5,000,000! Wells was very excited, and can't help sharing this thought. The secret number is X, and Wells has purchase N lottery tickets a1,a2,a3....aNa1,a2,a3....aN but has not received them yet. And if lucky enough, Wells could pick some numbers of them satisfy that b

1orb2orb3....orbk=Xb1orb2orb3....orbk=X, k is the amount of picked numbers.

How ever the owner of the lottery shop called SDJ, who decided to modify the lottery tickets and made Wells lost his fortune. In order to save energy to modify the lottery tickets, SDJ want to know the minimum amount of modification of lottery tickets.

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