Let $D=(V,A)$ be an $n$-vertex digraph with $n\ge 6$. For each vertex $v\in V$, let $a(v)$ be the degree of $v$ in $D$. Assume that for every pair of distinct vertices $x,y\in V$, the sum of their degrees satisfies $a(x)+a(y)\ge 3n+1$. For any two independent arcs $f_1,f_2\in A(D)$ and any integer partition $n=n_1+n_2$ where $n_1\ge 3$ and $n_2\ge 3$, $D$ contains two mutually vertex-disjoint dicycles $C_1$ and $C_2$ such that $|V(C_1)|=n_1$, $|V(C_2)|=n_2$, $f_1\in E(C_1)$, and $f_2\in E(C_2)$. Moreover, the condition is sharp.