Test:

1
1
1

And what is the answer if yes?

Answer is NO.

1
1
1
test is impossible
if a[i]=i then a[i]:=0 because
"Mummy has written down at ith position of the line the number of a child that the ith child pointed to, or 0 if the ith child suddenly confessed."
so
1
1
0
and answer is YES