const SIZE: usize = 31;

fn solve(factors: &Vec<Vec<usize>>) -> usize {
    let mut x = String::new();
    std::io::stdin().read_line(&mut x).ok();
    let x: usize = x.trim().parse().unwrap();
    let mut xfactors = vec![0usize; SIZE+1];
    let mut target = x;
    for i in 2..=SIZE {
        while target % i == 0 {
            target /= i;
            xfactors[i] += 1;
        }
    }
    for i in 2..=SIZE {
        let mut xcnt = 1usize;
        let mut fcnt = 1usize;
        for j in 2..=i {
            xcnt *= xfactors[j] + 1;
            fcnt *= xfactors[j] + factors[i][j] + 1;
        }
        if xcnt * 2 == fcnt {
            return x * i;
        }
    }
    x
}

fn main() {
    let mut t = String::new();
    std::io::stdin().read_line(&mut t).ok();
    let t: usize = t.trim().parse().unwrap();
    let mut result = Vec::with_capacity(t);
    let mut factors = vec!{vec![0usize; SIZE+1]; SIZE+1};
    for i in 2..=SIZE {
        let mut target = i;
        for j in 2..=SIZE {
            while target % j == 0 {
                target /= j;
                factors[i][j] += 1;
            }
        }
    }
    for _ in 0..t {
        result.push(solve(&factors));
    }
    for &v in result.iter() {
        println!("{}", v);
    }
}