SP9070 LIGHTIN - Lightning Conductor

Progressive climate change has forced the Byteburg authorities to build a huge lightning conductor that would protect all the buildings within the city. These buildings form a row along a single street, and are numbered from  to . The heights of the buildings and the lightning conductor are non-negative integers. Byteburg's limited funds allow construction of only a single lightning conductor. Moreover, as you would expect, the higher it will be, the more expensive. The lightning conductor of height  located on the roof of the building  (of height ) protects the building  (of height ) if the following inequality holds:  where  denotes the absolute value of the difference between  and . Byteasar, the mayor of Byteburg, asks your help. Write a program that, for every building , determines the minimum height of a lightning conductor that would protect all the buildings if it were put on top of the building . Input ----- In the first line of the standard input there is a single integer  () that denotes the number of buildings in Byteburg. Each of the following  lines holds a single integer  () that denotes the height of the -th building. Output ------ Your program should print out exactly  lines to the standard output. The -th line should give a non-negative integer  denoting the minimum height of the lightning conductor on the -th building. Example ------- For the input data: ``` 6 5 3 2 4 2 4 ``` the correct result is: ``` 2 3 5 3 5 4 ```

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