Sorry for making blog here. Actually I asked it as comment in announcement's page( Link ) on codeforces, but unfortunately no one replied.

So I decided to ask the same question as blog.

Can any one please the explain this line of editorial :

Here, if the elements in P are scanned from left to right, there must always be more left elements than right elements. The number of such arrangements corresponds to that of parenthesis sequences.

What I understood is that, lets say we have (1,2),(3,4),(5,6),(7,8) as corresponding (ai and bi).
Permutation : (1,2,4,3,5,6,7,8) have more right elements(2) than left elements(1) in first 3 elements (1,2,4) but still it can be divided it into two sequences A(1,3,5,7) and B(2,4,6,8), but in editorial it is told that it should not be possible ( as per I understood ) .
I know I have understood it wrong.
Anyone who did this problem or got the editorial please explain the line in blue

Editorial link : Link