Just like every fall, the organizers of the Southwestern
Europe Dice Simulation Contest are busy again this year. In
this edition you have to simulate a -sided die that outputs each of
three possible outcomes (which will be denoted by , and ) with a given probability, using
three dice in a given set. The simulation is performed this
way: you choose one of the given dice at random, roll it, and
report its outcome. You are free to choose the probabilities of
rolling each of the given dice, as long as each probability
is strictly greater than zero. Before distributing the
materials to the contestants, the organizers have to verify
that it is actually possible to solve this task.
For example, in the first test case of the sample input you
have to simulate a die that yields outcome , and with probabilities , and . We give you three dice, and in
this case the -th of
them always yields outcome , for each . Then it is possible to
simulate the given die in the following fashion: roll the first
die with probability , the second one with
probability and the
last one with probability .
Input
The input consists of at most test cases, separated by single
blank lines. Each test case consists of four lines: the first
three of them describe the three dice you are given and the
last one describes the die you have to simulate. Each of the
four lines contains 3 space-separated integers between
and inclusive. These numbers
will add up to ,
and represent
times the probability that rolling the die described in that
line yields outcome ,
and , respectively.
The test cases will finish with a line containing only the
number zero repeated three times (also preceded with a blank
line).
Output
For each case, your program should output a line with the
word YES if it is feasible to produce
the desired die from the given ones, and NO otherwise.
| Sample Input 1 |
Sample Output 1 |
0 0 10000
0 10000 0
10000 0 0
3000 4000 3000
0 0 10000
0 10000 0
3000 4000 3000
10000 0 0
0 0 0
|
YES
NO
|
