Wrong time and plot with day-accross using gnuplot

Question

By gnuplot, I plot two curves with time(like 23:59:23, means hour:minute:second) as xdata. But when the time steps to 00:00:00, the displayed xtics label and plots go wrong. Why and how to solve it?

MWE:

reset

#set border lt 4 
set key top horizontal
set ytics 1
set yrange [1:15]
set y2range [1:150]
unset y2tics
set y2tics nomirror
set y2tics 10
set grid
set format x "%H:%M:%S"
set xtics in offset 0,-0 rotate by -90
set style data linespoints

set datafile separator comma
set xdata time 
set timefmt "%H:%M:%S"

plot "x-time.txt" using 1:2 axes x1y1 title columnheader(2),"x-time.txt" using 1:3 axes x1y2 title columnheader(3)

Content of "x-time.txt":

time,value1,value2
23:59:49,1,1
23:59:50,2,4
23:59:51,3,9
23:59:52,4,16
23:59:53,5,25
23:59:54,6,36
23:59:55,7,49
23:59:56,8,64
23:59:57,9,81
23:59:58,10,100
23:59:59,11,121
00:00:00,12,144
00:00:01,13,169

PS: gnuplot v5.2.6 used

Answer 1

Change the last two entries in your input file

time,value1,value2
23:59:49,1,1
23:59:50,2,4
23:59:51,3,9
23:59:52,4,16
23:59:53,5,25
23:59:54,6,36
23:59:55,7,49
23:59:56,8,64
23:59:57,9,81
23:59:58,10,100
23:59:59,11,121
24:00:00,12,144
24:00:01,13,169

This is the result