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A. Magic Numbers

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA magic number is a number formed by concatenation of numbers 1, 14 and 144. We can use each of these numbers any number of times. Therefore 14144, 141414 and 1411 are magic numbers but 1444, 514 and 414 are not.

You're given a number. Determine if it is a magic number or not.

Input

The first line of input contains an integer *n*, (1 ≤ *n* ≤ 10^{9}). This number doesn't contain leading zeros.

Output

Print "YES" if *n* is a magic number or print "NO" if it's not.

Examples

Input

114114

Output

YES

Input

1111

Output

YES

Input

441231

Output

NO

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