fn main() { input!(p: u64); let k = (p - 1) / 2; let r = (1 + 2 * p - 16 * k % p - 4 * k * k % p) % p; let ans = if pow_mod(r, (p - 1) / 2, p) == 1 { "YES" } else { "NO" }; println!("{}", ans); } fn pow_mod(mut r: u64, mut n: u64, m: u64) -> u64 { let mut t = 1 % m; r %= m; while n > 0 { if n & 1 == 1 { t = t * r % m; } r = r * r % m; n >>= 1; } t } mod util { pub trait Join { fn join(self, sep: &str) -> String; } impl Join for I where I: Iterator, T: std::fmt::Display, { fn join(self, sep: &str) -> String { let mut s = String::new(); use std::fmt::*; for (i, v) in self.enumerate() { if i > 0 { write!(&mut s, "{}", sep).ok(); } write!(&mut s, "{}", v).ok(); } s } } } // ---------- begin input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 #[macro_export] macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } #[macro_export] macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); input_inner!{$iter $($r)*} }; } #[macro_export] macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, bytes) => { read_value!($iter, String).bytes().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // ---------- end input macro ---------- // floor(a ^ (1 / k)) pub fn kth_root(a: u64, k: u64) -> u64 { assert!(k > 0); if a == 0 { return 0; } if k >= 64 { return 1; } if k == 1 { return a; } let valid = |x: u64| -> bool { let mut t = x; for _ in 1..k { let (val, ok) = t.overflowing_mul(x); if !(!ok && val <= a) { return false; } t = val; } true }; let mut ok = 1; let mut ng = 2; while valid(ng) { ok = ng; ng *= 2; } while ng - ok > 1 { let mid = ok + (ng - ok) / 2; if valid(mid) { ok = mid; } else { ng = mid; } } ok }