In a Sankey diagram, a flow $F$ enters a node and splits into two output branches with widths $w_1 = pF$ and $w_2 = (1-p)F$. If the first branch $w_1$ undergoes a non-linear transformation such that the visual width $W_{vis} = \sqrt{w_1}$, and we require the total perceived visual width to be conserved ($W_{total} = W_{vis, 1} + W_{vis, 2}$), which condition must hold for the input flow $F$ if $p=0.5$?