You want to divide all integers from to into three piles, so that each integer belongs to exactly one pile.
Determine whether it is possible to make the sums of the three piles equal to in this order. If it is possible, output one such partition.
The order of the piles matters. The sum of the first pile must be , the sum of the second pile must be , and the sum of the third pile must be .
The input is given in the following format.
If it is possible, print on the first line.
Then print information about the three piles in the next lines. On the -th of these lines, first print the number of integers in the -th pile, followed by the integers in that pile separated by spaces.
The sum of the first pile is , the sum of the second pile is , and the sum of the third pile is .
The printed integers must contain every integer from to exactly once. The sums of the first, second, and third piles must be , respectively.
If it is impossible, print on the first line.
A pile with sum must contain the integer . Since there is only one such integer, it is impossible to make two piles both have sum .
