For each of the following program fragments, give an analysis of the running time.

for i in range$($n$)$:

for j in range$($i$,$n$**2)$:

for k in range$($j$)$:

sum$+=1$

for i in range$($n$)$:

for j in range$($i$,$n$**2)$:

if i $<$ j:

for k in range$($j$)$:

sum$+=1$

for i in range$($n$)$:

for j in range$($i$,$n$**2)$:

if i $==$ j:

for k in range$($j$)$:

sum$+=1$