use std::collections::*; use std::io::{Write, BufWriter}; // https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes.by_ref().map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr,) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, [ $t:tt ]) => {{ let len = read_value!($next, usize); read_value!($next, [$t; len]) }}; ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } // 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 } 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 nth(a: i64, n: i64) -> i64 { let mut pass = 0; let mut fail = std::cmp::min(a, 1 << ((60 + n - 1) / n)) + 1; while fail - pass > 1 { let mid = (fail + pass) / 2; let mut tmp = 1i64; for _ in 0..n { tmp = tmp.saturating_mul(mid); } if tmp <= a { pass = mid; } else { fail = mid; } } pass } fn is_sq(a: i64) -> bool { let s = nth(a, 2); s * s == a } fn main() { let out = std::io::stdout(); let mut out = BufWriter::new(out.lock()); macro_rules! puts {($($format:tt)*) => (let _ = write!(out,$($format)*););} input! { n: usize, a: [[i64]; n], } for mut a in a { let n = a.len(); loop { let mut changed = false; for i in 0..n { for j in 0..i { let g = pollard_rho::gcd(a[i], a[j]); if g != 1 { a[i] /= g; a[j] /= g; changed = true; } } } if !changed { break; } } puts!("{}\n", if a.into_iter().all(is_sq) { "Yes" } else { "No" }); } }