const LIMIT: 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 cnts = vec![0usize; LIMIT+1];
    let mut ret = LIMIT;
    let mut target = x;
    for i in 2..=LIMIT {
        while target % i == 0 {
            cnts[i] += 1;
            target /= i;
        }
    }
    for i in 2..LIMIT {
        let mut org = 1usize;
        let mut used = 1usize;
        for j in 2..=LIMIT {
            org *= cnts[j] + 1;
            used *= cnts[j] + 1 + factors[i][j];
        }
        if org * 2 == used {
            return i * x;
        }
    }
    ret * 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; LIMIT+1]; LIMIT+1];
    for i in 2..=LIMIT {
        let mut target = i;
        for j in 2..=LIMIT {
            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);
    }
}