These ten problems come from Chinese National Olympiad in Mathematics - Province Contest.

Problem 1 Polynomial P(x)=x⁵+a₁x⁴+a₂x³+a₃x²+a₄x+a₅, and we know when k=1, 2, 3, 4, P(k)=2007*k. Calculate P(10)-P(-5).

Problem 2 The sum of 100 positive integers a₁, a₂, ..., a₁₀₀ is 2007. Calculate the maximum possible value of .

Problem 3 Calculate 100101102103104......498499500 modulo 126.

Problem 4 We define the sum of the first n numbers of geometric progression {a_n} S_n. Now we know S₇=7, S₁₄=2014. Calculate S₇*(S₂₁-S₁₄).

Problem 5 Calculate the sum of this kind of positive integers n(n>=4): n satisfies that n! can be written as the product of n-3 consecutive positive integers.

Problem 6 Two vertices of a square are on the line y=2x-17, while the other two are on the parabola y=x². Calculate the sum of two different possible values of the area of this square.

Problem 7 A, B, C, D are four fixed points in the space and they are not on the same plane. Calculate the number of different parallelepipeds, which satisfies that 4 vertices of the parallelepiped are A, B, C and D.

Problem 8 Polynomial x²-x-1 exactly divides Polynomial a₁x¹⁷+a₂x¹⁶+1. Calculate a₁*a₂.

Problem 9 Suppose x is an acute angle, calculate the minimum possible value of (sin x +cos x)/(sin x +tan x) + (tan x +cot x)/(cos x +tan x) + (sin x +cos x)/(cos x +cot x) + (tan x +cot x)/(sin x +cot x).

Problem 10 Suppose x⁴+y⁴+z⁴=m/n, x, y, z are all real numbers, satisfying x*y+y*z+z*x=1 and 5*(x+1/x)=12*(y+1/y)=13*(z+1/z); m, n are positive integers and their greatest common divisor is 1. Calculate m+n.

Input

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Output

Ten lines, each contains a single integer denoted the answer to the correspoding problem.

Example

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