How to die? P94330

You are in front of a house just in the middle of a long street with n houses (for odd n). Every house is labeled with an integer number. Beyond the left-end of the street there is a deep see. Beyond the right-end of the street there is a hot desert. You are going to play a sadic game, where the only possible outcome is death. Every house number x tells you how many houses to the right you must walk (for a negative x you must walk to the left) before stopping and looking at a house number again. The rules are: If at some moment you happen to keep moving in a cycle, you will eventually die of tiredness. There is one exception: if you are going to be always in front of the same house, you will die of boredom. If you leave the street by the left end, you will drown. If you leave the street by the right end, you will die of thirst.

Please write a program to know how you are going to die.

Input

Input consists of several cases. Every case begins with n, followed by n integer numbers with absolute value at most 10⁸. Assume 1 ≤ n < 10⁵, and that n is odd.

Output

For every case, print how you are going to die.