Symmetric double counts

Consider: we know that the derviative of any sum of a collection of ones similar to the input.
because it is sum(xs) = x[1] + x[2] + ....

However for Symmetric it is giving 2 for the anti-diagonal on a 2x2 matrix.

using FiniteDifferences
using LinearAlgebra

grad(central_fdm(5, 1), sum, Symmetric(ones(2,2)))[1]
#== out:
2×2 Symmetric{Float64, Matrix{Float64}}:
 1.0  2.0
 2.0  1.0
 ==#


grad(central_fdm(5, 1), sum, ones(2,2))[1]
#==
2×2 Matrix{Float64}:
 1.0  1.0
 1.0  1.0
==#

Similar issues occur for prod which came up in https://github.com/JuliaDiff/ChainRules.jl/pull/335/files

Something must be wrong with out we are defining to_vec.
https://github.com/JuliaDiff/FiniteDifferences.jl/blob/266d6faa8039c382d3fbe80f8ef0b91f6a09726c/src/to_vec.jl#L90-L96

Reproduce the Symmetric and dense-matrix gradient examples from the issue, then inspect src/to_vec.jl around lines 90-96, where the issue identifies the suspected to_vec behavior. Compare the handling of Symmetric inputs with the expected sum and prod derivatives; done means the anti-diagonal is no longer double-counted and the shown examples produce the expected gradients.