An antique brass chronometer displays time using two independent rings of tiny indicator lamps instead of hands. The hour ring has 4 lamps, weighted 8, 4, 2, 1; whichever lamps are lit, their weights sum to the current hour, an integer from 0 to 11. The minute ring has 6 lamps, weighted 32, 16, 8, 4, 2, 1; the lit lamps on that ring sum to the current minute, an integer from 0 to 59. A restorer knows that exactly k lamps are lit across both rings combined, but the chronometer's glass is too fogged to see which ones. Determine every hour:minute reading that is consistent with exactly k lamps being lit in total.

Input format

A single line containing one integer k, the total number of lit lamps across both rings.

Output format

Print an integer C — the number of distinct valid readings — on the first line. Then print C more lines, one per reading, formatted as H:MM (the hour with no leading zero, the minute zero-padded to exactly two digits), sorted by hour ascending and then by minute ascending. Print no further lines if C is 0.

Constraints

• 0 <= k <= 10.

1

10
0:01
0:02
0:04
0:08
0:16
0:32
1:00
2:00
4:00
8:00

8

8
7:31
7:47
7:55
7:59
11:31
11:47
11:55
11:59