sample unique pairs from a matrix

I have a matrix of both negative and positive values that I would like
to randomly sample with the following 2 conditions:

1. only sample positive values
2. once a cell in the matrix has been sampled the row and column of
that cell cannot be sampled from again.

#some dummy data
set.seed(101)
dataf <- matrix(rnorm(36,1,2), nrow=6)

I can do this quite simply if all the values are positive by using the
sample function without replacement on the column and row indices.

samrow <- sample(6,replace=F)
samcol <- sample(6,replace=F)
values <- numeric(6)
for(i in 1:6){
   values[i] <- dataf[samrow[i], samcol[i]]
}

However, I am not sure how to include the logical condition to only
include postitive values