[Python] How to replace one of the levels of a MultiIndex dataframe with one of its columns

I have a multiindex dataframe such as

multiindex = pd.MultiIndex.from_arrays(
[list('aaaaasssssddddd'), [*range(3, 8), *range(1, 6), *range(2, 7)]],
names=['contract', 'index']
)
df = pd.DataFrame(np.random.randn(15, 3), index=multiindex, columns=list('zxc'))
>>>
z x c
contract index
a 3 0.354879 0.206557 0.308081
4 0.822102 -0.425685 1.973288
5 -0.801313 -2.101411 -0.707400
6 -0.740651 -0.564597 -0.975532
7 -0.310679 0.515918 -1.213565
s 1 -0.175135 0.777495 0.100466
2 2.295485 0.381226 -0.242292
3 -0.753414 1.172924 0.679314
4 -0.029526 -0.020714 1.546317
5 0.250066 -1.673020 -0.773842
d 2 -0.602578 -0.761066 -1.117238
3 -0.935758 0.448322 -2.135439
4 0.808704 -0.604837 -0.319351
5 0.321139 0.584896 -0.055951
6 0.041849 -1.660013 -2.157992


Now I want to replace the index of index with the column c. That is to say, I want the result as

z x
contract c
a 0.308081 0.354879 0.206557
1.973288 0.822102 -0.425685
-0.707400 -0.801313 -2.101411
-0.975532 -0.740651 -0.564597
-1.213565 -0.310679 0.515918
s 0.100466 -0.175135 0.777495
-0.242292 2.295485 0.381226
0.679314 -0.753414 1.172924
1.546317 -0.029526 -0.020714
-0.773842 0.250066 -1.673020
d -1.117238 -0.602578 -0.761066
-2.135439 -0.935758 0.448322
-0.319351 0.808704 -0.604837
-0.055951 0.321139 0.584896
-2.157992 0.041849 -1.660013


I implement it in one way

df.reset_index().set_index(['contract', 'c']).drop(['index'], axis=1)


But it seems there are some duplicate steps because I manipulate the index three times. Is there is a more elegant way to achieve that?

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