Problem B - Counting 1s
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Zaphod, a rather strange friend of yours from a different planet, is
interested in finding a number n that is equal to the number of 1s
in the decimal digits of all numbers <= n. In other words, if you
write all numbers from 1 to n, you will need to write the digit 1 n
times. 

Input
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Input consists of multiple lines, one line per case.  Each line contains
a single positive integer between 1 and 10^18 inclusive. There are no
leading zeros for these numbers. Input is terminated by a line containing 0.

Output
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For each case, print one line containing the string YES if the input is
a number that will satisfy Zaphod. Print NO otherwise.

Sample Input
------------

1
10
42
90210
199981
0

Output for sample input
-----------------------

YES
NO
NO
NO
YES