You are given a regular polygon with n vertices labeled from 1 to n in counter-clockwise order. The triangulation of a given polygon is a set of triangles such that each vertex of each triangle is a vertex of the initial polygon, there is no pair of triangles such that their intersection has non-zero area, and the total area of all triangles is equal to the area of the given polygon. The weight of a triangulation is the sum of weigths of triangles it consists of, where the weight of a triagle is denoted as the product of labels of its vertices.

Calculate the minimum weight among all triangulations of the polygon.

Input

The first line contains single integer n (3 ≤ n ≤ 500) — the number of vertices in the regular polygon.

Output

Print one integer — the minimum weight among all triangulations of the given polygon.

Examples

Input


3


Output


6


Input


4


Output


18

Note

According to Wiki: polygon triangulation is the decomposition of a polygonal area (simple polygon) P into a set of triangles, i. e., finding a set of triangles with pairwise non-intersecting interiors whose union is P.

In the first example the polygon is a triangle, so we don't need to cut it further, so the answer is 1 ⋅ 2 ⋅ 3 = 6.

In the second example the polygon is a rectangle, so it should be divided into two triangles. It's optimal to cut it using diagonal 1-3 so answer is 1 ⋅ 2 ⋅ 3 + 1 ⋅ 3 ⋅ 4 = 6 + 12 = 18.
#! /usr/bin/python

# memory = {}
# def getRes(i, j):
# 	if j - i == 1:
# 		return 0

# 	if (i, j) in memory:
# 		return memory[(i, j)]

# 	minVal = (i + 1)*(i + 2)*(j + 1) + getRes(i + 1, j)
# 	for k in range(i + 2, j):
# 		val = (i + 1)*(k + 1)*(j + 1) + getRes(i, k) + getRes(k, j)
# 		if val < minVal:
# 			minVal = val

# 	memory[(i, j)] = minVal
# 	return minVal

# memoryEnd = {}
# def getEnd(i, n):
# 	if n - i == 1:
# 		return 0

# 	if (i, n) in memoryEnd:
# 		return memoryEnd[(i, n)]

# 	minVal = (i + 1)*(i + 2)*1 + getEnd(i + 1, n)
# 	for k in range(i + 2, n):
# 		val = (i + 1)*(k + 1)*1 + getRes(i, k) + getEnd(k, n)
# 		if val < minVal:
# 			minVal = val

# 	memoryEnd[(i, n)] = minVal
# 	return minVal

# def getTotal(n):
# 	minScore = 1*2*3 + getEnd(2, n)
# 	for j in range(3, n):
# 		for i in range(1, j):
# 			score = 1*(i + 1)*(j + 1) + getRes(0, i) + getRes(i, j) + getEnd(j, n)
# 			if score < minScore:
# 				minScore = score
# 	return minScore

# from sys import argv
# maxN = int(argv[1])

# for n in range(3, maxN + 1):
# 	print getTotal(n)

result = [6, 18, 38, 68, 110, 166, 238, 328, 438, 570, 726, 908, 1118, 1358, 1630, 1936, 2278, 2658, 3078, 3540, 4046, 4598, 5198, 5848, 6550, 7306, 8118, 8988, 9918, 10910, 11966, 13088, 14278, 15538, 16870, 18276, 19758, 21318, 22958, 24680, 26486, 28378, 30358, 32428, 34590, 36846, 39198, 41648, 44198, 46850, 49606, 52468, 55438, 58518, 61710, 65016, 68438, 71978, 75638, 79420, 83326, 87358, 91518, 95808, 100230, 104786, 109478, 114308, 119278, 124390, 129646, 135048, 140598, 146298, 152150, 158156, 164318, 170638, 177118, 183760, 190566, 197538, 204678, 211988, 219470, 227126, 234958, 242968, 251158, 259530, 268086, 276828, 285758, 294878, 304190, 313696, 323398, 333298, 343398, 353700, 364206, 374918, 385838, 396968, 408310, 419866, 431638, 443628, 455838, 468270, 480926, 493808, 506918, 520258, 533830, 547636, 561678, 575958, 590478, 605240, 620246, 635498, 650998, 666748, 682750, 699006, 715518, 732288, 749318, 766610, 784166, 801988, 820078, 838438, 857070, 875976, 895158, 914618, 934358, 954380, 974686, 995278, 1016158, 1037328, 1058790, 1080546, 1102598, 1124948, 1147598, 1170550, 1193806, 1217368, 1241238, 1265418, 1289910, 1314716, 1339838, 1365278, 1391038, 1417120, 1443526, 1470258, 1497318, 1524708, 1552430, 1580486, 1608878, 1637608, 1666678, 1696090, 1725846, 1755948, 1786398, 1817198, 1848350, 1879856, 1911718, 1943938, 1976518, 2009460, 2042766, 2076438, 2110478, 2144888, 2179670, 2214826, 2250358, 2286268, 2322558, 2359230, 2396286, 2433728, 2471558, 2509778, 2548390, 2587396, 2626798, 2666598, 2706798, 2747400, 2788406, 2829818, 2871638, 2913868, 2956510, 2999566, 3043038, 3086928, 3131238, 3175970, 3221126, 3266708, 3312718, 3359158, 3406030, 3453336, 3501078, 3549258, 3597878, 3646940, 3696446, 3746398, 3796798, 3847648, 3898950, 3950706, 4002918, 4055588, 4108718, 4162310, 4216366, 4270888, 4325878, 4381338, 4437270, 4493676, 4550558, 4607918, 4665758, 4724080, 4782886, 4842178, 4901958, 4962228, 5022990, 5084246, 5145998, 5208248, 5270998, 5334250, 5398006, 5462268, 5527038, 5592318, 5658110, 5724416, 5791238, 5858578, 5926438, 5994820, 6063726, 6133158, 6203118, 6273608, 6344630, 6416186, 6488278, 6560908, 6634078, 6707790, 6782046, 6856848, 6932198, 7008098, 7084550, 7161556, 7239118, 7317238, 7395918, 7475160, 7554966, 7635338, 7716278, 7797788, 7879870, 7962526, 8045758, 8129568, 8213958, 8298930, 8384486, 8470628, 8557358, 8644678, 8732590, 8821096, 8910198, 8999898, 9090198, 9181100, 9272606, 9364718, 9457438, 9550768, 9644710, 9739266, 9834438, 9930228, 10026638, 10123670, 10221326, 10319608, 10418518, 10518058, 10618230, 10719036, 10820478, 10922558, 11025278, 11128640, 11232646, 11337298, 11442598, 11548548, 11655150, 11762406, 11870318, 11978888, 12088118, 12198010, 12308566, 12419788, 12531678, 12644238, 12757470, 12871376, 12985958, 13101218, 13217158, 13333780, 13451086, 13569078, 13687758, 13807128, 13927190, 14047946, 14169398, 14291548, 14414398, 14537950, 14662206, 14787168, 14912838, 15039218, 15166310, 15294116, 15422638, 15551878, 15681838, 15812520, 15943926, 16076058, 16208918, 16342508, 16476830, 16611886, 16747678, 16884208, 17021478, 17159490, 17298246, 17437748, 17577998, 17718998, 17860750, 18003256, 18146518, 18290538, 18435318, 18580860, 18727166, 18874238, 19022078, 19170688, 19320070, 19470226, 19621158, 19772868, 19925358, 20078630, 20232686, 20387528, 20543158, 20699578, 20856790, 21014796, 21173598, 21333198, 21493598, 21654800, 21816806, 21979618, 22143238, 22307668, 22472910, 22638966, 22805838, 22973528, 23142038, 23311370, 23481526, 23652508, 23824318, 23996958, 24170430, 24344736, 24519878, 24695858, 24872678, 25050340, 25228846, 25408198, 25588398, 25769448, 25951350, 26134106, 26317718, 26502188, 26687518, 26873710, 27060766, 27248688, 27437478, 27627138, 27817670, 28009076, 28201358, 28394518, 28588558, 28783480, 28979286, 29175978, 29373558, 29572028, 29771390, 29971646, 30172798, 30374848, 30577798, 30781650, 30986406, 31192068, 31398638, 31606118, 31814510, 32023816, 32234038, 32445178, 32657238, 32870220, 33084126, 33298958, 33514718, 33731408, 33949030, 34167586, 34387078, 34607508, 34828878, 35051190, 35274446, 35498648, 35723798, 35949898, 36176950, 36404956, 36633918, 36863838, 37094718, 37326560, 37559366, 37793138, 38027878, 38263588, 38500270, 38737926, 38976558, 39216168, 39456758, 39698330, 39940886, 40184428, 40428958, 40674478, 40920990, 41168496, 41416998, 41666498]

n = int(raw_input())

print result[n - 3]