FIBPOS - Fibonacci Terms

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The Fibonacci sequence is a sequence of integers in which each number is equal to the sum of the two preceding numbers. The first two integers in the sequence are both 1. Formally:

  • F1 = 1
  • F2 = 1
  • Fi = Fi-1 + Fi-2 for each i > 2

The beginning of this sequence is 1, 1, 2, 3, 5, 8, 13, 21.

We'll define the Fibonacci position of an integer greater than or equal to 1 as follows:

  • The Fibonacci position of 1 is 2 (since F2 = 1)
  • The Fibonacci position of any integer n > 1 such that Fi = n is i
  • The Fibonacci position of any integer n > 1 such that it is strictly between Fi and Fi+1 is i+(n-Fi)/(Fi+1-Fi) (informally, this means it is linearly distributed between Fi and Fi+1)

As examples, if FP(n) is the Fibonacci position of n,

  • FP(1) = 2 (first rule)
  • FP(5) = 5 (second rule F5 = 5)
  • FP(4) = 4.5 (third rule, is right in the middle of F4 = 3 and F5 = 5)

Given an integer n, find its Fibonacci position as a double.

Input

First line contains T <= 10. The following N lines each contain an integer 1 <= n <= 108.

Output

For each test case, print the Fibonacci position of n, rounded to 6 places of decimal.

Example

Input:
4
1
5
4
100

Output:
2.000000
5.000000
4.500000
11.200000


Added by:Mahesh Chandra Sharma
Date:2011-01-28
Time limit:0.100s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64