Cow Photography

The cows are feeling especially mischievous today. Farmer John just wants a photograph of his cows standing in a line, but they keep shifting position right before he can press the shutter.

Farmer John's $N$ ($1 \le N \le 20{,}000$) cows are tagged with ID numbers $1 \ldots N$. He wants to photograph them standing in one specific order, given by an array $A[1 \ldots N]$, where $A[j]$ is the ID of the $j$-th cow in that order. He lines the cows up in this order, but just before he can take the picture, up to one cow moves to a new spot in the line. More precisely, either no cow moves, or exactly one cow leaves her current spot and re-inserts herself somewhere else in the line.

Undeterred, Farmer John lines the cows up in the order $A$ again, and again, just before the shutter, up to one cow (different from the first) moves. This repeats until he has taken a total of five photographs, and then he gives up.

Each photograph therefore shows the order $A$ after up to one cow has moved. Crucially, if a cow chooses to actively move in one photograph, she does not actively move in any of the other four (although she may still end up in a different position because other cows moved around her).

Given all five photographs, reconstruct the intended order $A$. The intended order $A$ is always uniquely determined.

• Line 1: the number of cows, $N$ ($1 \le N \le 20{,}000$).
• The next $5N$ lines: five orderings, each given as a block of $N$ consecutive lines. Each line holds one cow ID, an integer in $1 \ldots N$. The $i$-th block is the $i$-th photograph.

• $N$ lines: the intended order $A$, one cow ID per line, from the front of the line to the back.

• In every photograph at most one cow actively changes position, and any cow that actively moves does so in exactly one of the five photographs.
• Under these rules the intended order $A$ is uniquely determined, so exactly one correct output exists.