Define the simple skewness of a collection of numbers to be the collection's mean minus its median. You are given a list of *n* (not necessarily distinct) integers. Find the non-empty subset (with repetition) with the maximum simple skewness.

The mean of a collection is the average of its elements. The median of a collection is its middle element when all of its elements are sorted, or the average of its two middle elements if it has even size.
The first line of the input contains a single integer *n* (1 ≤ *n* ≤ 200 000) — the number of elements in the list.

The second line contains *n* integers *x*<sub class="lower-index">*i*</sub> (0 ≤ *x*<sub class="lower-index">*i*</sub> ≤ 1 000 000) — the *i*th element of the list.
In the first case, the optimal subset is <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/04cdbd07a0375de9c557422eca077386392a9349.png" style="max-width: 100.0%;max-height: 100.0%;"/>, which has mean 5, median 2, and simple skewness of 5 - 2 = 3.

In the second case, the optimal subset is <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/af49670de7c27def20edf0ec421d9bb17d904c94.png" style="max-width: 100.0%;max-height: 100.0%;"/>. Note that repetition is allowed.

In the last case, any subset has the same median and mean, so all have simple skewness of 0.
4
1 2 3 12
3
1 2 12 
4
1 1 2 2
3
1 1 2 
2
1 2
2
1 2
1
1000000
1
1000000 
20
999999 999998 999996 999992 999984 999968 999936 999872 999744 999488 998976 997952 995904 991808 983616 967232 934464 868928 737856 475712
1
475712 
21
999999 999998 999996 999992 999984 999968 999936 999872 999744 999488 998976 997952 995904 991808 983616 967232 934464 868928 737856 475712 1000000
1
475712 
40
999999 999999 999998 999998 999996 999996 999992 999992 999984 999984 999968 999968 999936 999936 999872 999872 999744 999744 999488 999488 998976 998976 997952 997952 995904 995904 991808 991808 983616 983616 967232 967232 934464 934464 868928 868928 737856 737856 475712 0
3
737856 737856 999999 
1
534166
1
534166 
1
412237
1
412237 
1
253309
1
253309 
1
94381
1
94381 
1
935454
1
935454 
2
847420 569122
2
847420 569122
2
725491 635622
2
725491 635622
2
566563 590441
2
566563 590441
2
407635 619942
2
407635 619942
2
248707 649443
2
248707 649443
3
198356 154895 894059
3
154895 198356 894059 
3
76427 184396 963319
3
76427 184396 963319 
3
880502 176898 958582
1
176898 
3
758573 206400 991528
1
206400 
3
599645 198217 986791
1
198217 
4
549294 703669 96824 126683
3
96824 126683 703669 
4
390366 733171 92086 595244
3
92086 390366 733171 
4
231438 762672 125033 26806
3
26806 125033 762672 
4
109509 792173 120296 495368
3
109509 120296 792173 
4
950582 784676 190241 964614
1
190241 
5
900232 289442 225592 622868 113587
3
113587 225592 900232 
5
741304 281944 258539 54430 284591
3
281944 284591 741304 
5
582376 311446 253801 560676 530279
3
253801 311446 582376 
5
460447 303948 286063 992238 738282
3
286063 303948 992238 
5
301519 370449 319010 460799 983970
3
301519 319010 983970 
21
999999 999998 999996 999992 999984 999968 999936 999872 999744 999488 998976 997952 995904 991808 983616 967232 934464 868928 737856 475712 999998
3
999998 999998 999999 
print("_RANDOM_GUESS_1692458257.6628294")# 1692458257.6628468