use std::io::Read; fn get_word() -> String { let stdin = std::io::stdin(); let mut stdin=stdin.lock(); let mut u8b: [u8; 1] = [0]; loop { let mut buf: Vec = Vec::with_capacity(16); loop { let res = stdin.read(&mut u8b); if res.unwrap_or(0) == 0 || u8b[0] <= b' ' { break; } else { buf.push(u8b[0]); } } if buf.len() >= 1 { let ret = String::from_utf8(buf).unwrap(); return ret; } } } #[allow(dead_code)] fn get() -> T { get_word().parse().ok().unwrap() } // https://judge.yosupo.jp/submission/5155 mod pollard_rho { /// binary gcd pub fn gcd(mut x: i64, mut y: i64) -> i64 { if y == 0 { return x; } if x == 0 { return y; } let k = (x | y).trailing_zeros(); y >>= k; x >>= x.trailing_zeros(); while y != 0 { y >>= y.trailing_zeros(); if x > y { let t = x; x = y; y = t; } y -= x; } x << k } fn add_mod(x: i64, y: i64, n: i64) -> i64 { let z = x + y; if z >= n { z - n } else { z } } fn mul_mod(x: i64, mut y: i64, n: i64) -> i64 { assert!(x >= 0); assert!(x < n); let mut sum = 0; let mut cur = x; while y > 0 { if (y & 1) == 1 { sum = add_mod(sum, cur, n); } cur = add_mod(cur, cur, n); y >>= 1; } sum } pub fn mod_pow(x: i64, mut e: i64, n: i64) -> i64 { let mut prod = if n == 1 { 0 } else { 1 }; let mut cur = x % n; while e > 0 { if (e & 1) == 1 { prod = mul_mod(prod, cur, n); } e >>= 1; if e > 0 { cur = mul_mod(cur, cur, n); } } prod } pub fn is_prime(n: i64) -> bool { if n <= 1 { return false; } let small = [2, 3, 5, 7, 11, 13]; if small.iter().any(|&u| u == n) { return true; } if small.iter().any(|&u| n % u == 0) { return false; } let mut d = n - 1; let e = d.trailing_zeros(); d >>= e; // https://miller-rabin.appspot.com/ let a = [2, 325, 9375, 28178, 450775, 9780504, 1795265022]; a.iter().all(|&a| { if a % n == 0 { return true; } let mut x = mod_pow(a, d, n); if x == 1 { return true; } for _ in 0..e { if x == n - 1 { return true; } x = mul_mod(x, x, n); if x == 1 { return false; } } x == 1 }) } fn pollard_rho(n: i64, c: &mut i64) -> i64 { // An improvement with Brent's cycle detection algorithm is performed. // https://maths-people.anu.edu.au/~brent/pub/pub051.html if n % 2 == 0 { return 2; } loop { let mut x: i64; // tortoise let mut y = 2; // hare let mut d = 1; let cc = *c; let f = |i| add_mod(mul_mod(i, i, n), cc, n); let mut r = 1; // We don't perform the gcd-once-in-a-while optimization // because the plain gcd-every-time algorithm appears to // outperform, at least on judge.yosupo.jp :) while d == 1 { x = y; for _ in 0..r { y = f(y); d = gcd((x - y).abs(), n); if d != 1 { break; } } r *= 2; } if d == n { *c += 1; continue; } return d; } } /// Outputs (p, e) in p's ascending order. pub fn factorize(x: i64) -> Vec<(i64, usize)> { if x <= 1 { return vec![]; } let mut hm = std::collections::HashMap::new(); let mut pool = vec![x]; let mut c = 1; while let Some(u) = pool.pop() { if is_prime(u) { *hm.entry(u).or_insert(0) += 1; continue; } let p = pollard_rho(u, &mut c); pool.push(p); pool.push(u / p); } let mut v: Vec<_> = hm.into_iter().collect(); v.sort(); v } } // mod pollard_rho fn get_per(p: i64, e: usize) -> i64 { use pollard_rho::*; if p == 2 || p == 5 { return 1; } let facs = factorize(p - 1); let mut ans = p - 1; for &(q, _) in &facs { while ans % q == 0 && mod_pow(10, ans / q, p) == 1 { ans /= q; } } let mut x = p; for _ in 0..e - 1 { x *= p; ans *= p; } while ans % p == 0 && mod_pow(10, ans / p, x) == 1 { ans /= p; } ans } fn main() { use pollard_rho::*; let t: usize = get(); for _ in 0..t { let n: i64 = get(); let pe = factorize(n); let mut ans = 1; for (p, e) in pe { let per = get_per(p, e); let g = gcd(ans, per); ans /= g; ans *= per; } println!("{}", ans); } }