import std.stdio, std.array, std.string, std.conv, std.algorithm;
import std.typecons, std.range, std.random, std.math, std.container;
import std.numeric, std.bigint, core.bitop;

void main() {
    auto T = readln.chomp.to!int;

    long[] P;
    auto table = new bool[](10^^6);
    for (long i = 2; i * i <= 10L^^11; ++i) {
        if (table[i.to!int]) continue;
        P ~= i;
        for (long j = i * 2; j * j <= 10L ^^ 11; j += i) {
            table[j.to!int] = true;
        }
    }

    long[long] Q;

    while (T--) {
        auto X = readln.chomp.to!long;
        Q.clear();
        foreach (i; 0..P.length.to!int) {
            if (X % P[i] != 0) {
                long acm = 1;
                foreach (c; Q.values()) acm *= c + 1;
                long ans = min(X * P[i], dfs(1, X, acm, Q.keys().array, Q, P[i], acm));
                ans.writeln;
                break;
            } else {
                long count = 0;
                long Y = X;
                while (Y % P[i] == 0) {
                    Y /= P[i];
                    count += 1;
                }
                Q[P[i]] = count;
            }
        }
    }
}

long dfs(long cur, long X, long original, long[] P, long[long] count, long maxP, long acm) {
    if (cur >= maxP) {
        return 1L << 59;
    }
    if (original * 2 == acm) {
        return cur;
    }
    if (original * 2 < acm) {
        return 1L << 59;
    }
    if (X == 1) {
        return 1L << 59;
    }
    long ans = 1L << 59;
    foreach (p; P) if (X % p == 0) {
        acm /= count[p] + 1;
        count[p] += 1;
        acm *= count[p] + 1;
        ans = min(ans, dfs(cur * p, X / p, original, P, count, maxP, acm));
        acm /= count[p] + 1;
        count[p] -= 1;
        acm /= count[p] + 1;
    }
    return ans;
}