attractiveness worth of an is meant as: ∑i=1n∑j=1ngcd(ai,aj)⋅gcd(i,j) where gcd(x,y) signifies the best normal divisor (GCD) of integers x and y. At the end of the day, the beauty

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Chanek has a cluster an of n integers. The attractiveness worth of an is meant as: ∑i=1n∑j=1ngcd(ai,aj)⋅gcd(i,j) where gcd(x,y) signifies the best normal divisor (GCD) of integers x and y. At the end of the day, the beauty worth of a cluster an is the all out amount of gcd(ai,aj)⋅gcd(i,j) for all sets (i,j). Help Mr. Chanek discover the attractiveness worth of a, and output the outcome modulo 109+7! 

Input :the principal line contains an integer n (2≤n≤105). The subsequent line contains n integers a1,a2,… ,an (1≤ai≤105). 

Output :Output an integer signifying the beauty worth of a modulo 109+7.

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