Numbers with Invariant Tail by Squaring

Notice the following interesting relation for these 3-digit numbers:

625² = 390 625 = 625   mod 1000
376² = 141 376 = 376   mod 1000

Notice also that if an n-digit number a has the property a² = a   mod 10ⁿ, then also b = 10ⁿ + 1 – a has the same property, b² = b   mod 10ⁿ. Indeed,

b2   mod 10n	=	(10n + 1 – a)2   mod 10n
	=	(1 – a)2   mod 10n
	=	1 – 2a + a2   mod 10n
	=	1 – 2a + a   mod 10n
	=	1 – a   mod 10n
	=	10n + 1 – a   mod 10n
	=	b   mod 10n

This explains the connection 625 + 376 = 1001.

Question: Are there numbers having 1000 digits that are equal to their square   mod 10¹⁰⁰⁰?

Input Specification

There is no input for this problem.

Output Specification

Print the text “NO” if there are no such numbers. If there exist such numbers, print the first 10 digits of each such number on a separate line.