Find the minimum value in a range, WITH conditions

Ok, so here is my data:

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What I want to achieve is to find the minimum value in the bottom row, however columns that have "YES" in the top row should be ignored when calculating the minimum, (so in the example above the minimum in the second row would be 3, as the 1 in the BLUE column is ignored).

In addition to this, some, all, or none of the bottom row could have the text "Inf." instead of a value. In my data this represents 'Infinite' so can effectively be ignored.

Finally, to highlight an issue I have had, if all of the bottom row are "Inf." then running MIN() against the bottom row will return 0, however in this situation that is obviously misleading.

Thanks all, I hope to learn something here

Always the way... find out how to do it just after posting

Anyway, here is my solution.

Assuming the top left cell of the data is in B2.
I am going to use the value of 1000 to represent Infinity as that is good enough for what I am doing

Entered as an Array Formula into another cell:

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Thanks anyway