Synonymous Words Number System
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Synonymous Words Number System (SWNS) uses the lines of N characters consisting of '0' and '1' (2 ≤N≤ 10000). There is only one operation with words within the number system – it's called synonymization. Synonymization is reversing the character order in any substring containing even number of '1' symbols.

If we can create one word from the another one, by carrying out not more than 16·N synonymization, then such words are called synonyms.

It is necessary to determine whether the given words are synonymous, and, if so, find out the right sequence of synonymizations.

Input

Different words with a length of N characters are written in two lines, one per line.

Output

If the given words are not synonymous, output 'NO' in a single line.

Otherwise, output 'YES' in the first line. The second line contains an integer K (K≤ 16·N) – a number of synonymization required for the conversion. The following K lines contain pairs of numbers that describe conversion of the first word into the second one. The first integer specifies a number of the first character participating in synonymization, and the second integer (always greater than the first one) – a number of the last character.

Examples

Input

    110001111
    111100011

Output

    YES
    1
    3 7

Input

    110
    010

Output

    NO