题目描述

Displeased with Farmer John's leadership, the cows have seceded from the farm and have formed the first Continental Cowngress. Built on the principle of 'every cow gets something they want,' they've decided on the following voting system:
The M (1 <= M <= 4000) cows in attendance will vote on N (1 <= N <= 1,000) legislative bills. Each cow casts a 'yes' or 'no' vote (denoted as 'Y' or 'N' in the input file) on exactly two (distinct) bills B_i and C_i (1 <= B_i <= N; 1 <= C_i <= N). The votes are called VB_i (VB_i in {'Y', 'N'}) and VC_i (VC_i in {'Y', 'N'}) respectively.
Finally, the bills are to be passed or not in such a way that every cow gets her way on at least one of her votes. For example, if Bessie votes 'yes' on Bill 1, and 'no' on Bill 2, then in any valid solution, it must be the case that either Bill 1 gets passed or Bill 2 gets rejected (or both).
Given the votes of each of the cows, it's your job to figure out which bills will be passed and which bills will be rejected in order to conform to the rules above. If there is no solution, print 'IMPOSSIBLE'. If there is at least one solution, then for each bill, display:
Y if in every solution this bill passes
N if in every solution this bill fails
? if there are solutions where this bill passes and solutions where it does not pass
Consider the following set of votes (two for each cow): 
BILL - - - - -
1 2 3
Cow 1 YES NO
Cow 2 NO NO
Cow 3 YES YES
Cow 4 YES YES
From this, two solutions satisfy every cow:
Bill 1 passes (this then satisfies cows 1, 3, and 4) 
Bill 2 fails (this then satisfies cow 2) 
Bill 3 could pass or fail (and this is the reason there are two solutions) 
In fact, these are the only two solutions, so the answer is the three character string below:
YN?
由于对Farmer John的领导感到极其不悦，奶牛们退出了农场，组建了奶牛议会。
议会以“每头牛 都可以获得自己想要的”为原则，建立了下面的投票系统： M只到场的奶牛 (1 <= M <= 4000) 会给N个议案投票(1 <= N <= 1,000) 。每只 奶牛会对恰好两个议案 B_i and C_i (1 <= B_i <= N; 1 <= C_i <= N)投 出“是”或“否”（输入文件中的'Y'和'N'）。
他们的投票结果分别为VB_i (VB_i in {'Y', 'N'}) and VC_i (VC_i in {'Y', 'N'})。 最后，议案会以如下的方式决定：每只奶牛投出的两票中至少有一票和最终结果相符合。 例如Bessie给议案1投了赞成'Y'，给议案2投了反对'N'，那么在任何合法的议案通过 方案中，必须满足议案1必须是'Y'或者议案2必须是'N'（或者同时满足）。
给出每只奶牛的投票，你的工作是确定哪些议案可以通过，哪些不能。
如果不存在这样一个方案， 输出"IMPOSSIBLE"。
如果至少有一个解，输出： Y 如果在每个解中，这个议案都必须通过 N 如果在每个解中，这个议案都必须驳回 ? 如果有的解这个议案可以通过，有的解中这个议案会被驳回

输入格式：

Line 1: Two space-separated integers: N and M
Lines 2..M+1: Line i+1 describes cow i's votes with four
space-separated fields -- an integer, a vote, another integer, and another vote: B_i, VB_i, C_i, VC_i

输出格式：

Line 1: A string with N characters, where the ith character is either a 'Y' if the ith bill must pass, an 'N' if the ith bill must fail, or a '?' if it cannot be determined whether the bill passes from these votes.
If there is no solution which satisfies every cow, then output the single line 'IMPOSSIBLE'.

输入样例#1：

3 4 
1 Y 2 N 
1 N 2 N 
1 Y 3 Y 
1 Y 2 Y 

输出样例#1：

YN?