3 Paths

For a given binary grid $A$ of size $N \times N$, we define $f(A)$ as the number of distinct right-down paths that can be taken from $(1, 1)$ to $(N, N)$ such that all the cells $(i, j)$ you visit have $A[i][j] = 1$. A right-down path means that from the cell $(X, Y)$ you can go to either $(X + 1, Y)$ or $(X, Y + 1)$. Construct a grid $A$ with exactly $3$ paths, or claim there does not exist any