#[allow(unused_imports)]
#[cfg(feature = "dbg")]
use dbg::lg;

fn main() {
    let mut buf = ngtio::with_stdin();
    for _ in 0..buf.usize() {
        let n = buf.u64();
        for x in 2.. {
            let mut num = 1;
            let mut den = 1;
            {
                let mut x = x;
                for p in 2.. {
                    if x == 1 {
                        break;
                    }
                    let mut mul_x = 0;
                    while x % p == 0 {
                        mul_x += 1;
                        x /= p;
                    }
                    let mut n = n;
                    let mut mul_n = 0;
                    while n % p == 0 {
                        mul_n += 1;
                        n /= p;
                    }
                    den *= 1 + mul_n;
                    num *= 1 + mul_n + mul_x;
                }
            }
            if den * 2 == num {
                println!("{}", n * x);
                break;
            }
        }
    }
}

// template {{{
#[cfg(not(feature = "dbg"))]
#[allow(unused_macros)]
#[macro_export]
macro_rules! lg {
    ($($expr:expr),*) => {};
}
#[allow(dead_code)]
mod ngtio {
    mod i {
        pub use self::{
            multi_token::{Leaf, Parser, ParserTuple, RawTuple, Tuple, VecLen},
            token::{Token, Usize1},
        };
        use std::{
            io::{self, BufRead},
            iter,
        };
        pub fn with_stdin() -> Tokenizer<io::BufReader<io::Stdin>> {
            io::BufReader::new(io::stdin()).tokenizer()
        }
        pub fn with_str(src: &str) -> Tokenizer<&[u8]> {
            src.as_bytes().tokenizer()
        }
        pub struct Tokenizer<S: BufRead> {
            queue: Vec<String>, // FIXME: String のみにすると速そうです。
            scanner: S,
        }
        macro_rules! prim_method {
            ($name:ident: $T:ty) => {
                pub fn $name(&mut self) -> $T {
                    <$T>::leaf().parse(self)
                }
            };
            ($name:ident) => {
                prim_method!($name: $name);
            };
        }
        macro_rules! prim_methods {
            ($name:ident: $T:ty; $($rest:tt)*) => {
                prim_method!($name:$T);
                prim_methods!($($rest)*);
            };
            ($name:ident; $($rest:tt)*) => {
                prim_method!($name);
                prim_methods!($($rest)*);
            };
            () => ()
        }
        impl<S: BufRead> Tokenizer<S> {
            pub fn token(&mut self) -> String {
                self.load();
                self.queue.pop().expect("入力が終了したのですが。")
            }
            pub fn new(scanner: S) -> Self {
                Self {
                    queue: Vec::new(),
                    scanner,
                }
            }
            fn load(&mut self) {
                while self.queue.is_empty() {
                    let mut s = String::new();
                    let length = self.scanner.read_line(&mut s).unwrap(); // 入力が UTF-8 でないときにエラーだそうです。
                    if length == 0 {
                        break;
                    }
                    self.queue = s.split_whitespace().rev().map(str::to_owned).collect();
                }
            }
            pub fn skip_line(&mut self) {
                assert!(
                    self.queue.is_empty(),
                    "行の途中で呼ばないでいただきたいです。現在のトークンキュー: {:?}",
                    &self.queue
                );
                self.load();
            }
            pub fn end(&mut self) {
                self.load();
                assert!(self.queue.is_empty(), "入力はまだあります！");
            }
            pub fn parse<T: Token>(&mut self) -> T::Output {
                T::parse(&self.token())
            }
            pub fn parse_collect<T: Token, B>(&mut self, n: usize) -> B
            where
                B: iter::FromIterator<T::Output>,
            {
                iter::repeat_with(|| self.parse::<T>()).take(n).collect()
            }
            pub fn tuple<T: RawTuple>(&mut self) -> <T::LeafTuple as Parser>::Output {
                T::leaf_tuple().parse(self)
            }
            pub fn vec<T: Token>(&mut self, len: usize) -> Vec<T::Output> {
                T::leaf().vec(len).parse(self)
            }
            pub fn vec_tuple<T: RawTuple>(
                &mut self,
                len: usize,
            ) -> Vec<<T::LeafTuple as Parser>::Output> {
                T::leaf_tuple().vec(len).parse(self)
            }
            pub fn vec2<T: Token>(&mut self, height: usize, width: usize) -> Vec<Vec<T::Output>> {
                T::leaf().vec(width).vec(height).parse(self)
            }
            pub fn vec2_tuple<T>(
                &mut self,
                height: usize,
                width: usize,
            ) -> Vec<Vec<<T::LeafTuple as Parser>::Output>>
            where
                T: RawTuple,
            {
                T::leaf_tuple().vec(width).vec(height).parse(self)
            }
            prim_methods! {
                u8; u16; u32; u64; u128; usize;
                i8; i16; i32; i64; i128; isize;
                f32; f64;
                char; string: String;
            }
        }
        mod token {
            use super::multi_token::Leaf;
            use std::{any, fmt, marker, str};
            pub trait Token: Sized {
                type Output;
                fn parse(s: &str) -> Self::Output;
                fn leaf() -> Leaf<Self> {
                    Leaf(marker::PhantomData)
                }
            }
            impl<T> Token for T
            where
                T: str::FromStr,
                <Self as str::FromStr>::Err: fmt::Debug,
            {
                type Output = Self;
                fn parse(s: &str) -> Self::Output {
                    s.parse().unwrap_or_else(|_| {
                        panic!("Parse error!: ({}: {})", s, any::type_name::<Self>(),)
                    })
                }
            }
            pub struct Usize1 {}
            impl Token for Usize1 {
                type Output = usize;
                fn parse(s: &str) -> Self::Output {
                    usize::parse(s)
                        .checked_sub(1)
                        .expect("Parse error! (Zero substruction error of Usize1)")
                }
            }
        }
        mod multi_token {
            use super::{Token, Tokenizer};
            use std::{io::BufRead, iter, marker};
            pub trait Parser: Sized {
                type Output;
                fn parse<S: BufRead>(&self, server: &mut Tokenizer<S>) -> Self::Output;
                fn vec(self, len: usize) -> VecLen<Self> {
                    VecLen { len, elem: self }
                }
            }
            pub struct Leaf<T>(pub(super) marker::PhantomData<T>);
            impl<T: Token> Parser for Leaf<T> {
                type Output = T::Output;
                fn parse<S: BufRead>(&self, server: &mut Tokenizer<S>) -> T::Output {
                    server.parse::<T>()
                }
            }
            pub struct VecLen<T> {
                pub len: usize,
                pub elem: T,
            }
            impl<T: Parser> Parser for VecLen<T> {
                type Output = Vec<T::Output>;
                fn parse<S: BufRead>(&self, server: &mut Tokenizer<S>) -> Self::Output {
                    iter::repeat_with(|| self.elem.parse(server))
                        .take(self.len)
                        .collect()
                }
            }
            pub trait RawTuple {
                type LeafTuple: Parser;
                fn leaf_tuple() -> Self::LeafTuple;
            }
            pub trait ParserTuple {
                type Tuple: Parser;
                fn tuple(self) -> Self::Tuple;
            }
            pub struct Tuple<T>(pub T);
            macro_rules! impl_tuple {
                ($($t:ident: $T:ident),*) => {
                    impl<$($T),*> Parser for Tuple<($($T,)*)>
                        where
                            $($T: Parser,)*
                            {
                                type Output = ($($T::Output,)*);
#[allow(unused_variables)]
                                fn parse<S: BufRead >(&self, server: &mut Tokenizer<S>) -> Self::Output {
                                    match self {
                                        Tuple(($($t,)*)) => {
                                            ($($t.parse(server),)*)
                                        }
                                    }
                                }
                            }
                    impl<$($T: Token),*> RawTuple for ($($T,)*) {
                        type LeafTuple = Tuple<($(Leaf<$T>,)*)>;
                        fn leaf_tuple() -> Self::LeafTuple {
                            Tuple(($($T::leaf(),)*))
                        }
                    }
                    impl<$($T: Parser),*> ParserTuple for ($($T,)*) {
                        type Tuple = Tuple<($($T,)*)>;
                        fn tuple(self) -> Self::Tuple {
                            Tuple(self)
                        }
                    }
                };
            }
            impl_tuple!();
            impl_tuple!(t1: T1);
            impl_tuple!(t1: T1, t2: T2);
            impl_tuple!(t1: T1, t2: T2, t3: T3);
            impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4);
            impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5);
            impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5, t6: T6);
            impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5, t6: T6, t7: T7);
            impl_tuple!(
                t1: T1,
                t2: T2,
                t3: T3,
                t4: T4,
                t5: T5,
                t6: T6,
                t7: T7,
                t8: T8
            );
        }
        trait Scanner: BufRead + Sized {
            fn tokenizer(self) -> Tokenizer<Self> {
                Tokenizer::new(self)
            }
        }
        impl<R: BufRead> Scanner for R {}
    }
    pub use self::i::{with_stdin, with_str};
    mod prelude {
        pub use super::i::{Parser, ParserTuple, RawTuple, Token, Usize1};
    }
}
// }}}