A partition of a positive integer N is a sequence of integers which sum to N, usually written with plussigns between the numbers of the partition. For example
15 = 1+2+3+4+5 = 1+2+1+7+1+2+1
A partition is palindromic if it reads the same forward and backward. The first partition in the exampleis not palindromic while the second is. If a partition containing m integers is palindromic, its left half isthe first floor(m/2) integers and its right half is the last floor(m/2) integers (which must be thereverse of the left half. (floor(x) is the greatest integer less than or equal to x.)
A partition is recursively palindromic if it is palindromic and its left half is recursively palindromic orempty. Note that every integer has at least two recursively palindromic partitions one consisting of allones and a second consisting of the integer itself. The second example above is also recursivelypalindromic.
For example, the recursively palindromic partitions of 7 are:
7, 1+5+1, 2+3+2, 1+1+3+1+1, 3+1+3, 1+1+1+1+1+1+1
Write a program which takes as input an integer N and outputs the number of recursively palindromicpartitions of N.
The first line of input contains a single integer N, (1 ￡ N ￡ 1000) which is the number of data sets thatfollow. Each data set consists of a single line of input containing a single positive integer for whichthe number of recursively palindromic partitions is to be found.
For each data set, you should generate one line of output with the following values: The data setnumber as a decimal integer (start counting at one), a space and the number of recursivelypalindromic partitions of the input value.
本题由旧版NOJ导入，来源：ACM ICPC Greater New York Region 2008