I was thinking of this problem.

You have a matrix of size n by n (n<=10^5). You have to support q<=10^5 operations of 3 types (online):

Given (i, l, r, x), set a[i][l...r] to x

Given (l, r, x), set a[1...n][l...r] to x

Given (i, l, r), find the minimum of a[i][l...r]

Is there any way to support these operations efficiently?