In a place in Southwestern Europe, the name of which I do
not wish to recall, not long ago there were cities connected by unidirectional
roads, with possibly more than one road connecting a city to
another one, or even to itself. As a homework assignment for
your geography class, you need to calculate the number of paths
of length exactly two that were between each pair of cities.
However, you’ve been too busy celebrating the Spanish victory
in the World Cup, so now you are copying the answers from your
friend. You would like to make sure his answers are correct
before handing in your homework.
Input
The input consists of at most test cases, separated by single
blank lines. Each test case begins with a line containing the
integer (). The
following lines
contain elements each,
with element of line
being the number of
roads from city to
city (a number between
and , inclusive). After that, there
will be lines. Each
will contain elements,
with element of line
being the answer from
your friend for the number of length- paths from city to city ; it will be an integer between
and inclusive.
The test cases will finish with a line containing only the
number zero (also preceded by a blank line).
Note:
Large input file; use fast I/O routines.
Output
For each case, your program should output a line. The
content of this line should be YES if
your classmate’s solution to the assignment is right, and
NO otherwise.
| Sample Input 1 |
Sample Output 1 |
3
2 0 1
1 0 3
1 1 0
5 1 2
5 3 1
3 0 4
3
2 0 1
1 0 3
1 1 0
5 1 2
5 3 2
3 0 4
0
|
YES
NO
|
