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Root of the equation

Time limit = 1 second(s)

Solve the equation

x^(x^(x^(x^( ... infinite ... )))) = A

where x is a positive real number.

Right side of the equation is limit of Fn(x) as n tends to infinity where

Fn(x) = x^(x^(x^(x^( ... n times ... ))));

Input The real number A (number of given digits less then 20).

Output If there is no root, output NO. Otherwise output the root (only one) with accuracy 10^(-19).

Input#1
1000
Output#1
NO
Input#2
1.5
Output#2
1.3103706971044483036

Author:
Voroztsov Artem
7 November 2004

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