λ-calculus tuple rotl problem

tuple_rotl.txt

Implement a λ-Term named `rotL` that, when applied to a function F, a Church Nat
N, and a Church N-Tuple, returns the same Church N-Tuple, but with elements
shifted left. In other words, create a generic 'rotL<N,F,t>' function for
N-tuples. Example:
- (rotL λf.λx.(f (f x))     λt.(t 1 2))   == λt.(t 2 1)
- (rotL λf.λx.(f (f (f x))) λt.(t 1 2 3)) == λt.(t 2 3 1)
Your final answer must be a λ-Term that implements `rotL` correctly, as follows:
@rotL = term_here

NOTE: Don't omit parenthesis. Each application requires them. Example:
- WRONG: λf. λx. f (f x)
- RIGHT: λf. λx. (f (f x))
- WRONG: (λx. f x) λx.x
- RIGHT: (λx.(f x) λx.x)
- WRONG: λf. λx. λy. (f x y)
- RIGHT: λf. λx. λy. ((f x) y)

ANSWER:

Interesting. I would have assumed it to find the obvious solution for n-1

n=>t=>k=>t(x=>n(q=>r=>s=>q(r(s)))(u=>u(x))(k))

and adapt it such that it increments the Church n separately or sth
(which is basically what it does, now that I think about it)

Not sure it matters, but fyi such solutions are part of bruijn's standard library (e.g. here), so it might be baked into the model already