Andrew and Jerry are playing a game with Harry as the scorekeeper. The game consists of three rounds. In each round, Andrew and Jerry draw randomly without replacement from a jar containing *n* balls, each labeled with a distinct positive integer. Without looking, they hand their balls to Harry, who awards the point to the player with the larger number and returns the balls to the jar. The winner of the game is the one who wins at least two of the three rounds.

Andrew wins rounds 1 and 2 while Jerry wins round 3, so Andrew wins the game. However, Jerry is unhappy with this system, claiming that he will often lose the match despite having the higher overall total. What is the probability that the sum of the three balls Jerry drew is strictly higher than the sum of the three balls Andrew drew?
The first line of input contains a single integer *n* (2 ≤ *n* ≤ 2000) — the number of balls in the jar.

The second line contains *n* integers *a*<sub class="lower-index">*i*</sub> (1 ≤ *a*<sub class="lower-index">*i*</sub> ≤ 5000) — the number written on the *i*th ball. It is guaranteed that no two balls have the same number.
In the first case, there are only two balls. In the first two rounds, Andrew must have drawn the 2 and Jerry must have drawn the 1, and vice versa in the final round. Thus, Andrew's sum is 5 and Jerry's sum is 4, so Jerry never has a higher total.

In the second case, each game could've had three outcomes — 10 - 2, 10 - 1, or 2 - 1. Jerry has a higher total if and only if Andrew won 2 - 1 in both of the first two rounds, and Jerry drew the 10 in the last round. This has probability <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/3c0ec296285f607c66d594132fb91e5e5f2bb007.png" style="max-width: 100.0%;max-height: 100.0%;"/>.
2
1 2
0.0000000000
3
1 2 10
0.0740740741
3
1 2 3
0.0000000000
4
2 4 1 3
0.0416666667
11
1 2 4 8 16 32 64 128 256 512 1024
0.2773433509
18
69 88 49 91 42 56 58 13 38 93 77 99 18 32 82 81 92 46
0.1974898208
16
14 34 22 53 11 40 50 12 91 86 32 75 36 33 41 9
0.2145798611
11
54 91 4 6 88 23 38 71 77 26 84
0.1890428249
20
11 37 81 56 61 2 26 27 59 69 24 7 71 76 45 54 89 17 95 20
0.1931218837
19
55 91 63 21 30 82 14 38 9 67 50 44 90 93 68 6 73 65 29
0.1920376960
13
1 2 4 8 16 32 64 128 256 512 1024 2048 4096
0.2881011986
15
1 2 3 4 5 10 20 40 80 160 320 640 1280 2560 5000
0.2950679192
4
1000 5000 1001 4999
0.0925925926
10
1000 1001 1002 1003 1004 1005 4001 4002 4003 4004
0.1796872428
n = int(input())
t = list(map(int, input().split()))

s, k = 0, 5001
d = [0, 0] * k

for a in t:
    for b in t: d[b - a] += 1
for i in range(k, 2 * k): d[i] += d[i - 1]

for i in range(1, k):
    s += d[i] * sum(d[j] * d[-1 - i - j] for j in range(1, k - i))

print(8 * s / (n * n - n) ** 3)