The given input sequence is $\{ 111, 333 , 243, 199, 234, 279, 119 \}$ and the hash table is of size $10$ with hash function $h(k) = k \mod 10$. When hash table uses quadratic probing with $h'(k)= h(k) + c_1 * i + c_2 * i^2, c_1 = 0, c_2 = 1$, the total number of collisions happening while mapping the given input sequence are __________.