We say that an integer 𝐷D is a divisor of another integer 𝐴A if the fraction 𝐴/𝐷A/D is also an integer. Given two positive integers 𝐴A and 𝐵B, compute the largest number which is a divisor of both 𝐴A and 𝐵B.

A certain number 1≤x≤1091≤𝑥≤109 is chosen. You are given two integers a𝑎 and b𝑏, which are the two largest divisors of the number x𝑥. At the same time, the condition 1≤a<b<x1≤𝑎<𝑏<𝑥 is satisfied.

Let's consider all integers in the range from 11 to n𝑛 (inclusive).Among all pairs of distinct integers in this range, find the maximum possible greatest common divisor of integers in pair. Formally, find the maximum value of gcd(a,b)gcd(𝑎,𝑏), where 1≤a<b≤n1≤𝑎<𝑏≤𝑛.The greatest common divisor, gcd(a,b)gcd(𝑎,𝑏), of two positive integers a𝑎 and b𝑏 is the biggest integer that is a divisor of both a𝑎 and b𝑏.InputThe first line contains a single integer t𝑡 (1≤t≤1001≤𝑡≤100)  — the number of test cases. The description of the test cases follows.The only line of each test case contains a single integer n𝑛 (2≤n≤1062≤𝑛≤106).OutputFor each test case, output the maximum value of gcd(a,b)gcd(𝑎,𝑏) among all 1≤a<b≤n1≤𝑎<𝑏≤𝑛.

You are given an integer x𝑥. Your task is to find any integer y𝑦 (1≤y<x)(1≤𝑦<𝑥) such that gcd(x,y)+ygcd(𝑥,𝑦)+𝑦 is maximum possible.Note that if there is more than one y𝑦 which satisfies the statement, you are allowed to find any.gcd(a,b)gcd(𝑎,𝑏) is the Greatest Common Divisor of a𝑎 and b𝑏. For example, gcd(6,4)=2gcd(6,4)=2.InputThe first line contains a single integer t𝑡 (1≤t≤10001≤𝑡≤1000) — the number of test cases.Each of the following t𝑡 lines contains a single integer x𝑥 (2≤x≤10002≤𝑥≤1000).OutputFor each test case, output any y𝑦 (1≤y<x1≤𝑦<𝑥), which satisfies the statement.ExampleinputCopy710721100210006outputCopy56189817503

What is the smallest positive integer whose proper divisors add up to more than the integer itself?

Sum of NDefine 𝑓(𝑋)f(X) as the largest divisor of 𝑋X other than 𝑋X itself. For example, 𝑓(12)=6f(12)=6 and 𝑓(7)=1f(7)=1.Note that 𝑓(1)f(1) is defined to be 00.Given an integer 𝐾K, find the sum of all 𝑁N such that 𝑓(𝑁)=𝐾f(N)=K.It can be shown that the answer does not exceed 101810 18 under the given constraints.Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of a single integer 𝐾K.Output FormatFor each test case, output on a new line, the sum of all 𝑁N which satisfy 𝑓(𝑁)=𝐾f(N)=K.Constraints1≤𝑇≤1041≤T≤10 4 2≤𝐾≤1062≤K≤10 6 Sample 1:InputOutput3231841536Explanation:Test Case 1 : The only number which has 𝑓(𝑁)=2f(N)=2 is 44.Test Case 2 : The only numbers which have 𝑓(𝑁)=3f(N)=3 are 66 and 99. The sum of them is 1515.