Let $R$ be a finite Riemann surface (having negative Euler Characteristic) without boundary (may have punctures) and $q$ be a unit area quadratic differential on $R$. We define $\mathcal{MF}_{1}=\{F \in \mathcal{MF} : Ext_{R}(F)=1\}$ and the function

$$I : \mathcal{MF}_{1} \rightarrow [0,+\infty]$$ as $I(F) = i(H(q),F) + i(V(q),F)$ for $F \in \mathcal{MF}_{1}$, where $\mathcal{MF}$ is the set of all measured foliations on $R$ upto Whitehead Equivalence, $Ext_{R}(F)$ is the extremal length of the foliation $F$ on $R$, $i(\cdot,\cdot)$ denotes the intersection number between measured foliations and $H(q), V(q)$ are respectively the horizontal and vertical foliations of $q$. Using Minsky's Inequality ($i(G,F)^{2} \le Ext_{R}(F)Ext_{R}(G)$) it is easy to see that $I(F) \le 2$ for all $F \in \mathcal{MF}_{1}$. Note that for the foliations $H(q)$ and $V(q)$ we have $I(H(q))=1=I(V(q))$. It seems that for a foliation $F \in \mathcal{MF}_{1}$ the more it intersects $H(q)$, the less it intersects $V(q)$. Can it be shown that $I$ is actually bounded by 1? If not, then what should be a counter example. Any help would be appreciated.