3-sided dice

时间限制:1s      空间限制:128MB

题目描述

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 3-sided die that outputs each of three possible outcomes (which will be denoted by 1, 2 and 3) 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 1, 2 and 3 with probabilities $ {\frac{{3}}{{10}}}$,$ {\frac{{4}}{{10}}}$ and $ {\frac{{3}}{{10}}}$. We give you three dice, and in this case the i-th of them always yields outcome i, for each i = 1, 2, 3. Then it is possible to simulate the given die in the following fashion: roll the first die with probability $ {\frac{{3}}{{10}}}$, the second one with probability $ {\frac{{4}}{{10}}}$ and the last one with probability $ {\frac{{3}}{{10}}}$.


一个骰子有3个面,3个面(A,B,C面)上分别有3个数字。在本题中,先给出了3个骰子,每个骰子给出3个面的数字。我们保证对于每个骰子,3个面的数字和为10000。之后再给出一个我们希望得到的A,B,C面的结果,然后希望你给3个骰子分配概率, 第一个骰子分配概率 p1,第二个p2,第三个p3,满足
(1) p1 + p2 + p3 = 1
(2) 3个骰子的每个面的期望和等于给出的那个面的期望的和

例如,样例1中
0 0 10000
0 10000 0
10000 0 0
骰子1: A(0), B(0), C(10000)
骰子2: A(0), B(10000), C(0)
骰子3: A(10000), B(0), C(0)
目标: A(3000) B(4000) C(3000)
于是我可以分配 p1 = 3/10, p2 = 4/10, p3 = 3/10
这样
A面期望: p1 * 0 + p2 * 0 + p3 * 10000 = 3000
B面期望: p1 * 0 + p2 * 10000 + p3 * 0 = 4000
C面期望: p1 * 10000 + p2 * 0 + p3 * 0 = 3000

在本题中,保证给出的3个数对的和均为10000。


输入格式

The input consists of several 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 0 and 10 000 inclusive. These numbers will add up to 10 000, and represent 10 000 times the probability that rolling the die described in that line yields outcome 1, 2 and 3, respectively.

The test cases will finish with a line containing only the number zero repeated three times (also preceded with a blank line).

输入多组数据,每组数据给出3个骰子的A,B,C面的 点数,然后给出一个期望的结果。
保证给出的3个数对的和均为10000。

如果遇到3个0,那么则表示数据结束


输出格式

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.


对于期望的数对,如果可以分配p1,p2,p3满足以上条件,则输出"YES"否则输出"NO"


样例输入

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




样例输出

YES
NO

提示

没有写明提示


题目来源

鸣谢 AekdyCoin