Consider the following sorting algorithm: == 1. def CoolSort(A[ ], low, high) 2. if (low high): /=1 3. do nothing 4. else if ((low+1) == high): /=2 5. place A[low] and A[low+1] in the correct relative order else: 7. m=[ 2(high-low+1)] 8. CoolSort(A, low, low+(m-1)) 9. CoolSort(A, high-m+1, high) 10. CoolSort(A, low, low+(m-1)) 6. a. Prove that CoolSort will sort correctly every input it is given. b. Analyze the running time of CoolSort