// ---------- begin xor segment tree ---------- pub struct XorSegmentTree { data: Vec>, e: T, op: F, size: usize, } impl XorSegmentTree where T: Clone, F: Fn(&T, &T) -> T, { pub fn new(a: Vec, e: T, op: F) -> Self { let size = a.len(); assert!(size.next_power_of_two() == size); let k = size.trailing_zeros() as usize / 2; let mut data = Vec::with_capacity(k + 1); data.push(a); for i in 1..=k { let mut a = Vec::with_capacity(size); for data in data.last().unwrap().chunks(1 << i) { let (l, r) = data.split_at(1 << (i - 1)); a.extend(l.iter().zip(r.iter()).map(|(l, r)| op(l, r))); a.extend(r.iter().zip(l.iter()).map(|(l, r)| op(l, r))); } data.push(a); } Self { data, e, op, size } } pub fn find(&self, mut l: usize, mut r: usize, xor: usize) -> T { assert!(l <= r && r <= self.size && xor < self.size); if l == r { return self.e.clone(); } let mut x = self.e.clone(); let mut y = self.e.clone(); for (shift, data) in self.data.iter().enumerate() { if l >> shift & 1 == 1 { x = (self.op)(&x, &data[l ^ xor]); l += 1 << shift; } if r >> shift & 1 == 1 { r -= 1 << shift; y = (self.op)(&data[r ^ xor], &y); } if l == r { return (self.op)(&x, &y); } } let k = self.data.len() - 1; l >>= k; r >>= k; let data = self.data.last().unwrap(); for i in l..r { x = (self.op)(&x, &data[(i << k) ^ xor]); } (self.op)(&x, &y) } fn update(&mut self, pos: usize, v: T) { assert!(pos < self.size); self.data[0][pos] = v; for shift in 1..self.data.len() { let s = (pos >> shift) << shift; let mut p = std::mem::take(&mut self.data[shift]); let c = &self.data[shift - 1][s..(s + (1 << shift))]; let (l, r) = c.split_at(1 << (shift - 1)); let ab = l.iter().zip(r.iter()).chain(r.iter().zip(l.iter())); for (p, (a, b)) in p[s..].iter_mut().zip(ab) { *p = (self.op)(a, b); } self.data[shift] = p; } } } // ---------- end xor segment tree ---------- // ---------- begin modint ---------- use std::marker::*; use std::ops::*; pub trait Modulo { fn modulo() -> u32; } pub struct ConstantModulo; impl Modulo for ConstantModulo<{ M }> { fn modulo() -> u32 { M } } pub struct ModInt(u32, PhantomData); impl Clone for ModInt { fn clone(&self) -> Self { Self::new_unchecked(self.0) } } impl Copy for ModInt {} impl Add for ModInt { type Output = ModInt; fn add(self, rhs: Self) -> Self::Output { let mut v = self.0 + rhs.0; if v >= T::modulo() { v -= T::modulo(); } Self::new_unchecked(v) } } impl AddAssign for ModInt { fn add_assign(&mut self, rhs: Self) { *self = *self + rhs; } } impl Sub for ModInt { type Output = ModInt; fn sub(self, rhs: Self) -> Self::Output { let mut v = self.0 - rhs.0; if self.0 < rhs.0 { v += T::modulo(); } Self::new_unchecked(v) } } impl SubAssign for ModInt { fn sub_assign(&mut self, rhs: Self) { *self = *self - rhs; } } impl Mul for ModInt { type Output = ModInt; fn mul(self, rhs: Self) -> Self::Output { let v = self.0 as u64 * rhs.0 as u64 % T::modulo() as u64; Self::new_unchecked(v as u32) } } impl MulAssign for ModInt { fn mul_assign(&mut self, rhs: Self) { *self = *self * rhs; } } impl Neg for ModInt { type Output = ModInt; fn neg(self) -> Self::Output { if self.is_zero() { Self::zero() } else { Self::new_unchecked(T::modulo() - self.0) } } } impl std::fmt::Display for ModInt { fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result { write!(f, "{}", self.0) } } impl std::fmt::Debug for ModInt { fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result { write!(f, "{}", self.0) } } impl Default for ModInt { fn default() -> Self { Self::zero() } } impl std::str::FromStr for ModInt { type Err = std::num::ParseIntError; fn from_str(s: &str) -> Result { let val = s.parse::()?; Ok(ModInt::new(val)) } } impl From for ModInt { fn from(val: usize) -> ModInt { ModInt::new_unchecked((val % T::modulo() as usize) as u32) } } impl From for ModInt { fn from(val: u64) -> ModInt { ModInt::new_unchecked((val % T::modulo() as u64) as u32) } } impl From for ModInt { fn from(val: i64) -> ModInt { let mut v = ((val % T::modulo() as i64) + T::modulo() as i64) as u32; if v >= T::modulo() { v -= T::modulo(); } ModInt::new_unchecked(v) } } impl ModInt { pub fn new_unchecked(n: u32) -> Self { ModInt(n, PhantomData) } pub fn zero() -> Self { ModInt::new_unchecked(0) } pub fn one() -> Self { ModInt::new_unchecked(1) } pub fn is_zero(&self) -> bool { self.0 == 0 } } impl ModInt { pub fn new(d: u32) -> Self { ModInt::new_unchecked(d % T::modulo()) } pub fn pow(&self, mut n: u64) -> Self { let mut t = Self::one(); let mut s = *self; while n > 0 { if n & 1 == 1 { t *= s; } s *= s; n >>= 1; } t } pub fn inv(&self) -> Self { assert!(!self.is_zero()); self.pow(T::modulo() as u64 - 2) } pub fn fact(n: usize) -> Self { (1..=n).fold(Self::one(), |s, a| s * Self::from(a)) } pub fn perm(n: usize, k: usize) -> Self { if k > n { return Self::zero(); } ((n - k + 1)..=n).fold(Self::one(), |s, a| s * Self::from(a)) } pub fn binom(n: usize, k: usize) -> Self { if k > n { return Self::zero(); } let k = k.min(n - k); let mut nu = Self::one(); let mut de = Self::one(); for i in 0..k { nu *= Self::from(n - i); de *= Self::from(i + 1); } nu * de.inv() } } // ---------- end modint ---------- // ---------- begin precalc ---------- pub struct Precalc { fact: Vec>, ifact: Vec>, inv: Vec>, } impl Precalc { pub fn new(n: usize) -> Precalc { let mut inv = vec![ModInt::one(); n + 1]; let mut fact = vec![ModInt::one(); n + 1]; let mut ifact = vec![ModInt::one(); n + 1]; for i in 2..=n { fact[i] = fact[i - 1] * ModInt::new_unchecked(i as u32); } ifact[n] = fact[n].inv(); if n > 0 { inv[n] = ifact[n] * fact[n - 1]; } for i in (1..n).rev() { ifact[i] = ifact[i + 1] * ModInt::new_unchecked((i + 1) as u32); inv[i] = ifact[i] * fact[i - 1]; } Precalc { fact, ifact, inv } } pub fn inv(&self, n: usize) -> ModInt { assert!(n > 0); self.inv[n] } pub fn fact(&self, n: usize) -> ModInt { self.fact[n] } pub fn ifact(&self, n: usize) -> ModInt { self.ifact[n] } pub fn perm(&self, n: usize, k: usize) -> ModInt { if k > n { return ModInt::zero(); } self.fact[n] * self.ifact[n - k] } pub fn binom(&self, n: usize, k: usize) -> ModInt { if k > n { return ModInt::zero(); } self.fact[n] * self.ifact[k] * self.ifact[n - k] } } // ---------- end precalc ---------- type M = ModInt>; // ---------- begin scannner ---------- #[allow(dead_code)] mod scanner { use std::str::FromStr; pub struct Scanner<'a> { it: std::str::SplitWhitespace<'a>, } impl<'a> Scanner<'a> { pub fn new(s: &'a String) -> Scanner<'a> { Scanner { it: s.split_whitespace(), } } pub fn next(&mut self) -> T { self.it.next().unwrap().parse::().ok().unwrap() } pub fn next_bytes(&mut self) -> Vec { self.it.next().unwrap().bytes().collect() } pub fn next_chars(&mut self) -> Vec { self.it.next().unwrap().chars().collect() } pub fn next_vec(&mut self, len: usize) -> Vec { (0..len).map(|_| self.next()).collect() } } } // ---------- end scannner ---------- use std::io::Write; fn main() { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); let mut sc = scanner::Scanner::new(&s); let out = std::io::stdout(); let mut out = std::io::BufWriter::new(out.lock()); run(&mut sc, &mut out); } fn run(sc: &mut scanner::Scanner, out: &mut std::io::BufWriter) { let n: usize = sc.next(); let s = sc.next_bytes(); let mut a = vec![M::one(); (1 << n) + 1]; let mut b = vec![M::one(); (1 << n) + 1]; for i in 1..a.len() { a[i] = M::new(2) * a[i - 1]; b[i] = M::new(11) * b[i - 1]; } type T = (M, u32); let merge = |l: &T, r: &T| -> T { (l.0 * b[r.1 as usize] + r.0 * a[l.1 as usize], l.1 + r.1) }; let a = s .iter() .map(|s| (M::new((*s - b'0') as u32), 1)) .collect::>(); let mut seg = XorSegmentTree::new(a, (M::zero(), 0), merge); let q: usize = sc.next(); for _ in 0..q { let op: u8 = sc.next(); if op == 1 { let x: usize = sc.next(); let y: u32 = sc.next(); seg.update(x, (M::new(y), 1)); } else { let l: usize = sc.next(); let r = sc.next::() + 1; let x: usize = sc.next(); let ans = seg.find(l, r, x).0; writeln!(out, "{}", ans).ok(); } } }