NDIVPHI2 - N DIV PHI_N (Hard)

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Given an integer N <= 1025000 find the smallest m <= N such that m/phi(m) is maximum. Where phi is Euler's totient function.

Input

The first line in the input gives the number of test cases T (T <= 200), and then T lines follow each containing an integer N.

Output

Output the smallest required value of m.

Example

Input:
1
10

Output:
6


Added by:SALVO
Date:2010-04-23
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:ADA95 ASM32 ASM64 BASH BF C CSHARP C++ 4.3.2 CPP CPP14 C99 CLPS LISP sbcl LISP clisp D ERL FORTRAN HASK ICON ICK JAVA JS-RHINO LUA NEM NICE OCAML PAS-GPC PAS-FPC PERL PHP PIKE PRLG-swi PYTHON RUBY SCALA SCM guile SCM qobi ST TCL TEXT WHITESPACE
Resource:Frank Rafael Arteaga