As you may know from the comic \Asterix and the Chieftain's Shield", Gergovia consists of one street,

and every inhabitant of the city is a wine salesman. You wonder how this economy works? Simple

enough: everyone buys wine from other inhabitants of the city. Every day each inhabitant decides how

much wine he wants to buy or sell. Interestingly, demand and supply is always the same, so that each

inhabitant gets what he wants.

There is one problem, however: Transporting wine from one house to another results in work. Since

all wines are equally good, the inhabitants of Gergovia don't care which persons they are doing trade

with, they are only interested in selling or buying a specic amount of wine. They are clever enough

to gure out a way of trading so that the overall amount of work needed for transports is minimized.

In this problem you are asked to reconstruct the trading during one day in Gergovia. For simplicity

we will assume that the houses are built along a straight line with equal distance between adjacent

houses. Transporting one bottle of wine from one house to an adjacent house results in one unit of

work.

Input

The input consists of several test cases. Each test case starts with the number of inhabitants n

(2 n 100000). The following line contains n integers ai (