You are given a beam balance and $N$ objects where $i^{th}$ object weighs $2^{i-1}$ , 0 < $i$<=$N$. $F(N)$ denotes the no. of ways of placing these objects(one by one) on balance such that the left side is always heavy (after every placement). Find the value of $F(100)$ and give the answer modulo $10^9 + 7$.