Detect whether a sequence of integers is an arithmetic series or not.

Input

Each line contains space separated numbers.

A line with only 0 is the end of input.

Output

'Yes' if input sequence is really an arithmetic series. 'No' otherwise.

Example

Input:
1 3 5 7
9 8 7 6 5 4
1 2 4 5
0

Output:
Yes
Yes
No