If I understand the question correctly...the idler gear doesn't matter. It can be anything that fits, and it won't change the final ratio. For instance, if you have
50 - 25 - 50, the 50:25 gives you 2:1, but then the 25:50 gives you 1:2, so the net is 1:1.
In your case, it's 50:65, then 65:50, but it still works out to 1:1.
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