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Byteasar urgently needs to measure milliliters of water. He went to a shop that sells technical glass. Unfortunately, water measuring glass is out of date and found the shop being wound up. Most of the glass was sold out and there were only two identical defective cylinders. Their defect was that each of them had only a subset of all the necessary scales (in milliliters). Byteasar had no choice: he needed those cylinders, so he bought them. He is facing a new problem now: how to measure milliliters of water using his cylinders?
In the beginning both cylinders are empty. Possible actions that can be performed are:
The first line of the input contains one positive integer () that represents the number of scales in each of the cylinders. The second line contains an increasing sequence of integers (separated by single spaces): the scales' values. is always equal to and () is equal to the capacity of each of the cylinders. The third and last line of the input contains one integer ().
If it is impossible for Byteasar to measure the desired amount of water, your program should output a single word NIE (Polish for no). Otherwise your program should output the minimal number of actions that are necessary to perform the measurement.
For the input data:
4 0 2 5 15 9
the correct result is:
Task author: Jakub Pawlewicz.