Lucky Number

A positive integer is defined as a Lucky Number by the following process. Consider the digits of the number from right to left (the units digit is the 1^st position, the tens digit is the 2^nd position, and so on). For digits in odd positions, perform the following transformation:

• Multiply the digit by 7.
• If the product is greater than 9, repeatedly replace the number by the sum of its digits until the result is not greater than 9. Formally, if a digit in an odd position is d, compute \( x = 7d \), then while \( x > 9 \), update \( x = \sum_{i} x_i \) (where \( x_i \) denotes the digits of \( x \)).

For digits in even positions, keep the digit unchanged. After transforming each digit according to its position, construct a new number using the transformed digits (maintaining the original positions). Finally, sum all the digits of this new number. If the total sum is a multiple of 8, then the original number is a Lucky Number.

Example: Consider the number \(16347\). Its digits (from right to left) are: 7 (1^st), 4 (2^nd), 3 (3^rd), 6 (4^th), and 1 (5^th). For odd positions:

• 1^st digit: \(7 \times 7 = 49\) \(\to 4+9=13 \to 1+3=4\).
• 3^rd digit: \(3 \times 7 = 21\) \(\to 2+1=3\).
• 5^th digit: \(1 \times 7 = 7\) (no further transformation needed as 7 \(\le 9\)).

For even positions, the digits remain the same. Thus, the transformed number is formed (from left to right) as \(7, 6, 3, 4, 4\) whose digit sum is \(7+6+3+4+4=24\), a multiple of 8. Therefore, \(16347\) is a Lucky Number.

inputFormat

The input consists of a single line containing a positive integer.

For example:

16347

outputFormat

Output a single line with YES if the number is a Lucky Number, and NO otherwise.

sample

16347

YES