Understanding Editorial of Google Kickstart round C- problem B

In Editorial of this question it is stated that “Once we have checked all rows, we check to see that every two-X row’s set of X columns pairs up with exactly one other two-X row’s set of X columns, and that no such pair shares any position with any other pair.”

My question is that since number of X is exactly 2*N-1. Why doesn’t it just sufficient to check that all row and column except one particular row and column should have exactly 2 ‘X’ and that exceptional row and column should have only one 1 ‘x’ ? Where does this logic fail??

.X…
…XX.
.X.X.
X.X…
X…X
This example satisfies your condition that all rows and columns except 1 should have exactly 2 Xs, but you wont be able to make a big X out of this. Hope this helps.

X.X…
X…X.
…X.X
.X.X.
.X…
This types of cases you would be missing in your solutions

Thanks!! Got it.

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