Time Limit: Java: 2000 ms / Others: 2000 ms

Memory Limit: Java: 65536 KB / Others: 65536 KB

Marsha and Bill own a collection of marbles. They want to split the collection
among themselves so that both receive an equal share of the marbles. This would
be easy if all the marbles had the same value, because then they could just split
the collection in half. But unfortunately, some of the marbles are larger, or
more beautiful than others. So, Marsha and Bill start by assigning a value, a
natural number between one and six, to each marble. Now they want to divide the
marbles so that each of them gets the same total value.

Unfortunately, they realize that it might be impossible to divide the marbles in this way (even if the total value of all marbles is even). For example, if there are one marble of value 1, one of value 3 and two of value 4, then they cannot be split into sets of equal value. So, they ask you to write a program that checks whether there is a fair partition of the marbles.

Each line in the input describes one collection of marbles to be divided. The
lines consist of six non-negative integers n1, n2, ..., n6, where ni is the
number of marbles of value i. So, the example from above would be described
by the input-line ``1 0 1 2 0 0''. The maximum total number of marbles will
be 20000.

The last line of the input file will be ``0 0 0 0 0 0''; do not process this line.

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