const LIMIT: usize = 31;

fn solve(cnt_map: &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 target = x;
    for i in 2..=LIMIT {
        while target % i == 0 {
            target /= i;
            cnts[i] += 1;
        }
    }
    for i in 2..=LIMIT {
        let mut org = 1usize;
        let mut times = 1usize;
        for j in 2..=LIMIT {
            org *= cnts[j] + 1;
            times *= cnts[j] + 1 + cnt_map[i][j];
        }
        if org * 2 == times {
            return i * x;
        }
    }
    LIMIT * x
}

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