// SNIPPET read
pub trait Readable {
    type Output;
    fn words_count() -> usize;
    fn read_words(words: &[&str]) -> Result<Self::Output, String>;
}
#[macro_export]
macro_rules! readable {
    ( $t:ty, $words_count:expr, |$words:ident| $read_words:expr ) => {
        impl Readable for $t {
            type Output = $t;
            fn words_count() -> usize { $words_count }
            fn read_words($words: &[&str]) -> Result<$t, String> {
                Ok($read_words)
            }
        }
    };
}
readable!((), 1, |_ss| ());
readable!(String, 1, |ss| ss[0].to_string());
impl Readable for char {
    type Output = char;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<char, String> {
        let chars: Vec<char> = words[0].chars().collect();
        if chars.len() == 1 {
            Ok(chars[0])
        } else {
            Err(format!("cannot parse `{}` as a char", words[0]))
        }
    }
}
pub struct Chars();
impl Readable for Chars {
    type Output = Vec<char>;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<Vec<char>, String> {
        Ok(words[0].chars().collect())
    }
}
impl Readable for i8 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<i8, String> {
        use std::str::FromStr;
        i8::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as {}", words[0], stringify!(i8))
        })
    }
}
impl Readable for u8 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<u8, String> {
        use std::str::FromStr;
        u8::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as {}", words[0], stringify!(u8))
        })
    }
}
impl Readable for i16 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<i16, String> {
        use std::str::FromStr;
        i16::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as {}", words[0], stringify!(i16))
        })
    }
}
impl Readable for u16 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<u16, String> {
        use std::str::FromStr;
        u16::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as {}", words[0], stringify!(u16))
        })
    }
}
impl Readable for i32 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<i32, String> {
        use std::str::FromStr;
        i32::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as {}", words[0], stringify!(i32))
        })
    }
}
impl Readable for u32 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<u32, String> {
        use std::str::FromStr;
        u32::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as {}", words[0], stringify!(u32))
        })
    }
}
impl Readable for i64 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<i64, String> {
        use std::str::FromStr;
        i64::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as {}", words[0], stringify!(i64))
        })
    }
}
impl Readable for u64 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<u64, String> {
        use std::str::FromStr;
        u64::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as {}", words[0], stringify!(u64))
        })
    }
}
impl Readable for isize {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<isize, String> {
        use std::str::FromStr;
        <isize>::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as {}", words[0], stringify!(isize))
        })
    }
}
impl Readable for usize {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<usize, String> {
        use std::str::FromStr;
        <usize>::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as {}", words[0], stringify!(usize))
        })
    }
}
impl Readable for f32 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<f32, String> {
        use std::str::FromStr;
        f32::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as {}", words[0], stringify!(usize))
        })
    }
}
impl Readable for f64 {
    type Output = Self;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<f64, String> {
        use std::str::FromStr;
        f64::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as {}", words[0], stringify!(usize))
        })
    }
}
#[allow(non_camel_case_types)]
pub struct u8_;
impl Readable for u8_ {
    type Output = u8;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        u8::read_words(words).map(|n| n-1)
    }
}
#[allow(non_camel_case_types)]
pub struct u16_;
impl Readable for u16_ {
    type Output = u16;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        u16::read_words(words).map(|n| n-1)
    }
}
#[allow(non_camel_case_types)]
pub struct u32_;
impl Readable for u32_ {
    type Output = u32;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        u32::read_words(words).map(|n| n-1)
    }
}
#[allow(non_camel_case_types)]
pub struct u64_;
impl Readable for u64_ {
    type Output = u64;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        u64::read_words(words).map(|n| n-1)
    }
}
#[allow(non_camel_case_types)]
pub struct usize_;
impl Readable for usize_ {
    type Output = usize;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        <usize>::read_words(words).map(|n| n-1)
    }
}
impl<T1: Readable, T2: Readable> Readable for (T1, T2) {
    type Output = (T1::Output, T2::Output);
    fn words_count() -> usize {
        T1::words_count() + T2::words_count()
    }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::words_count());
        let mut start = 0;
        let count1 = T1::words_count();
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let val2 = T2::read_words(&words[start..])?;
        Ok((val1, val2))
    }
}
impl<T1: Readable, T2: Readable, T3: Readable> Readable for (T1, T2, T3) {
    type Output = (T1::Output, T2::Output, T3::Output);
    fn words_count() -> usize {
        T1::words_count() + T2::words_count() + T3::words_count()
    }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::words_count());
        let mut start = 0;
        let count1 = T1::words_count();
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let count2 = T2::words_count();
        let val2 = T2::read_words(&words[start .. start+count2])?;
        start += count2;
        let val3 = T3::read_words(&words[start..])?;
        Ok((val1, val2, val3))
    }
}
impl<T1: Readable, T2: Readable, T3: Readable, T4: Readable> Readable for (T1, T2, T3, T4) {
    type Output = (T1::Output, T2::Output, T3::Output, T4::Output);
    fn words_count() -> usize {
        T1::words_count() + T2::words_count() + T3::words_count() + T4::words_count()
    }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::words_count());
        let mut start = 0;
        let count1 = T1::words_count();
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let count2 = T2::words_count();
        let val2 = T2::read_words(&words[start .. start+count2])?;
        start += count2;
        let count3 = T3::words_count();
        let val3 = T3::read_words(&words[start .. start+count3])?;
        start += count3;
        let val4 = T4::read_words(&words[start..])?;
        Ok((val1, val2, val3, val4))
    }
}
impl<T1: Readable, T2: Readable, T3: Readable, T4: Readable, T5: Readable> Readable for (T1, T2, T3, T4, T5) {
    type Output = (T1::Output, T2::Output, T3::Output, T4::Output, T5::Output);
    fn words_count() -> usize {
        T1::words_count() + T2::words_count() + T3::words_count() + T4::words_count() + T5::words_count()
    }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::words_count());
        let mut start = 0;
        let count1 = T1::words_count();
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let count2 = T2::words_count();
        let val2 = T2::read_words(&words[start .. start+count2])?;
        start += count2;
        let count3 = T3::words_count();
        let val3 = T3::read_words(&words[start .. start+count3])?;
        start += count3;
        let count4 = T4::words_count();
        let val4 = T4::read_words(&words[start .. start+count4])?;
        start += count4;
        let val5 = T5::read_words(&words[start..])?;
        Ok((val1, val2, val3, val4, val5))
    }
}
impl<T1: Readable, T2: Readable, T3: Readable, T4: Readable, T5: Readable, T6: Readable> Readable for (T1, T2, T3, T4, T5, T6) {
    type Output = (T1::Output, T2::Output, T3::Output, T4::Output, T5::Output, T6::Output);
    fn words_count() -> usize {
        T1::words_count() + T2::words_count() + T3::words_count() + T4::words_count() + T5::words_count() + T6::words_count()
    }
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::words_count());
        let mut start = 0;
        let count1 = T1::words_count();
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let count2 = T2::words_count();
        let val2 = T2::read_words(&words[start .. start+count2])?;
        start += count2;
        let count3 = T3::words_count();
        let val3 = T3::read_words(&words[start .. start+count3])?;
        start += count3;
        let count4 = T4::words_count();
        let val4 = T4::read_words(&words[start .. start+count4])?;
        start += count4;
        let count5 = T5::words_count();
        let val5 = T5::read_words(&words[start .. start+count5])?;
        start += count5;
        let val6 = T6::read_words(&words[start..])?;
        Ok((val1, val2, val3, val4, val5, val6))
    }
}
pub trait ReadableFromLine {
    type Output;
    fn read_line(line: &str) -> Result<Self::Output, String>;
}
fn split_into_words(line: &str) -> Vec<&str> {
    #[allow(deprecated)]
    line.trim_right_matches('\n').split_whitespace().collect()
}
impl<T: Readable> ReadableFromLine for T {
    type Output = T::Output;
    fn read_line(line: &str) -> Result<T::Output, String> {
        let words = split_into_words(line);
        if words.len() != T::words_count() {
            return Err(format!("line `{}` has {} words, expected {}",
                               line, words.len(), T::words_count()));
        }
        T::read_words(&words)
    }
}
fn read_words_into_vec<T: Readable>(words: &[&str], line: &str) -> Result<Vec<T::Output>, String> {
    let n = T::words_count();
    assert_eq!(words.len() % n, 0);
    let mut result = Vec::new();
    for chunk in words.chunks(n) {
        match T::read_words(chunk) {
            Ok(v) => result.push(v),
            Err(msg) => {
                let fragment_msg = if n == 1 {
                    format!("word {}", result.len())
                } else {
                    let l = result.len();
                    format!("words {}-{}", n*l + 1, (n+1) * l)
                };
                return Err(format!(
                    "{} of line `{}`: {}", fragment_msg, line, msg
                ));
            }
        }
    }
    Ok(result)
}
fn split_into_words_for_collection<T: Readable>(
    line: &str, prefix_words_count: usize
) -> Result<Vec<&str>, String> {
    let n = T::words_count();
    let words = split_into_words(line);
    if words.len() < prefix_words_count {
        return Err(
            format!("line `{}` has {} words, expected at least {}",
                    line, words.len(), prefix_words_count)
        );
    }
    if (words.len() - prefix_words_count) % T::words_count() != 0 {
        return Err(
            format!("line `{}` has {} words, expected {} + {}n",
                    line, words.len(), prefix_words_count, n)
        );
    }
    Ok(words)
}
#[macro_export]
macro_rules! readable_collection {
    ($u:ident => $collection_in:ty, $collection_out:ty) => {
        readable_collection!($u: [] => $collection_in, $collection_out);
    };
    ($u:ident : [ $( $bound:path ),* ] => $collection_in:ty, $collection_out:ty) => {
        impl<$u: Readable> ReadableFromLine for $collection_in
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = $collection_out;
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let words = split_into_words_for_collection::<$u>(line, 0)?;
                Ok(read_words_into_vec::<$u>(&words, line)?.into_iter().collect())
            }
        }
        impl<T1: Readable, $u: Readable> ReadableFromLine for (T1, $collection_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T1::Output, $collection_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let prefix_len = T1::words_count();
                let words = split_into_words_for_collection::<$u>(line, prefix_len)?;
                let val1 = T1::read_words(&words[..prefix_len])?;
                let rest = read_words_into_vec::<$u>(&words[prefix_len..], line)?;
                Ok((val1, rest.into_iter().collect()))
            }
        }
        impl<T1: Readable, T2: Readable, $u: Readable> ReadableFromLine for (T1, T2, $collection_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T1::Output, T2::Output, $collection_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let prefix_len = <(T1, T2)>::words_count();
                let words = split_into_words_for_collection::<$u>(line, prefix_len)?;
                let mut start = 0;
                let count1 = T1::words_count();
                let val1 = T1::read_words(&words[start .. start+count1])?;
                start += count1;
                let count2 = T2::words_count();
                let val2 = T2::read_words(&words[start .. start+count2])?;
                let rest = read_words_into_vec::<$u>(&words[prefix_len..], line)?;
                Ok((val1, val2, rest.into_iter().collect()))
            }
        }
        impl<T1: Readable, T2: Readable, T3: Readable, $u: Readable> ReadableFromLine for (T1, T2, T3, $collection_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T1::Output, T2::Output, T3::Output, $collection_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let prefix_len = <(T1, T2, T3)>::words_count();
                let words = split_into_words_for_collection::<$u>(line, prefix_len)?;
                let mut start = 0;
                let count1 = T1::words_count();
                let val1 = T1::read_words(&words[start .. start+count1])?;
                start += count1;
                let count2 = T2::words_count();
                let val2 = T2::read_words(&words[start .. start+count2])?;
                start += count2;
                let count3 = T3::words_count();
                let val3 = T3::read_words(&words[start .. start+count3])?;
                let rest = read_words_into_vec::<$u>(&words[prefix_len..], line)?;
                Ok((val1, val2, val3, rest.into_iter().collect()))
            }
        }
        impl<T1: Readable, T2: Readable, T3: Readable, T4: Readable, $u: Readable> ReadableFromLine for (T1, T2, T3, T4, $collection_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T1::Output, T2::Output, T3::Output, T4::Output, $collection_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let prefix_len = <(T1, T2, T3, T4)>::words_count();
                let words = split_into_words_for_collection::<$u>(line, prefix_len)?;
                let mut start = 0;
                let count1 = T1::words_count();
                let val1 = T1::read_words(&words[start .. start+count1])?;
                start += count1;
                let count2 = T2::words_count();
                let val2 = T2::read_words(&words[start .. start+count2])?;
                start += count2;
                let count3 = T3::words_count();
                let val3 = T3::read_words(&words[start .. start+count3])?;
                start += count3;
                let count4 = T4::words_count();
                let val4 = T4::read_words(&words[start .. start+count4])?;
                let rest = read_words_into_vec::<$u>(&words[prefix_len..], line)?;
                Ok((val1, val2, val3, val4, rest.into_iter().collect()))
            }
        }
    };
}
readable_collection!(U => Vec<U>, Vec<U::Output>);
pub fn read<T: ReadableFromLine>() -> T::Output {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    T::read_line(&line).unwrap()
}
#[macro_export]
macro_rules! read {
    () => {
        let mut line = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
    };
    ( $pat:pat = $t:ty ) => {
        let $pat = read::<$t>();
    };
    ( $( $pat:pat = $t:ty ),+ ) => {
        read!(($($pat),*) = ($($t),*));
    };
}
#[macro_export]
macro_rules! readls {
    ( $( $pat:pat = $t:ty ),+ ) => {
        $(
            read!($pat = $t);
        )*
    };
}
pub fn readx<T: ReadableFromLine>() -> Vec<T::Output> {
    use std::io::{self, BufRead};
    let stdin = io::stdin();
    let result = stdin.lock().lines().map(|line_result| {
        let line = line_result.expect("read from stdin failed");
        T::read_line(&line).unwrap()
    }).collect();
    result
}
#[macro_export]
macro_rules! readx_loop {
    ( |$pat:pat = $t:ty| $body:expr ) => {
        {
            use std::io::BufRead;
            let stdin = std::io::stdin();
            for line in stdin.lock().lines() {
                let line = line.expect("read from stdin failed");
                let $pat = <$t>::read_line(&line).unwrap();
                $body
            }
        }
    };
    ( |$($pat:pat = $t:ty),*| $body:expr ) => {
        readx_loop!(|($($pat),*) = ($($t),*)| $body);
    };
}
pub fn readn<T: ReadableFromLine>(n: usize) -> Vec<T::Output> {
    use std::io::{self, BufRead};
    let stdin = io::stdin();
    let result: Vec<T::Output> = stdin.lock().lines().take(n).map(|line_result| {
        let line = line_result.expect("read from stdin failed");
        T::read_line(&line).unwrap()
    }).collect();
    if result.len() < n {
        panic!("expected reading {} lines, but only {} lines are read",
               n, result.len());
    }
    result
}
#[macro_export]
macro_rules! readn_loop {
    ( $n:expr, |$pat:pat = $t:ty| $body:expr ) => {
        {
            use std::io::BufRead;
            let stdin = std::io::stdin();
            let mut lock = stdin.lock();
            for _ in 0..$n {
                let mut line = String::new();
                lock.read_line(&mut line).expect("read from stdin failed");
                let $pat = <$t>::read_line(&line).unwrap();
                $body
            }
        }
    };
    ( $n:expr, |$($pat:pat = $t:ty),*| $body:expr ) => {
        readn_loop!($n, |($($pat),*) = ($($t),*)| $body);
    };
}
pub trait Words {
    fn read<T: Readable>(&self) -> T::Output;
}
impl<'a> Words for [&'a str] {
    fn read<T: Readable>(&self) -> T::Output {
        T::read_words(self).unwrap()
    }
}
impl<'a> Words for &'a str {
    fn read<T: Readable>(&self) -> T::Output {
        T::read_words(&[self]).unwrap()
    }
}

// SNIPPET segtree
pub struct SegmentTree<T: Clone, F: Fn(&T, &T) -> T> {
    heap: Vec<T>,
    identity: T,
    aggregate: F
}
mod segment_tree_internal {
    pub fn parent_of(heap_index: usize) -> usize {
        (heap_index - 1) / 2
    }
    pub fn left_of(heap_index: usize) -> usize {
        heap_index * 2 + 1
    }
    pub fn right_of(heap_index: usize) -> usize {
        left_of(heap_index) + 1
    }
    pub fn is_root_or_right(heap_index: usize) -> bool {
        heap_index % 2 == 0
    }
}
impl<T: Clone, F: Fn(&T, &T) -> T> SegmentTree<T, F> {
    pub fn new(len: usize, identity: T, aggregate: F) -> SegmentTree<T, F> {
        SegmentTree {
            heap: vec![identity.clone(); (len * 2).saturating_sub(1)],
            identity: identity,
            aggregate: aggregate
        }
    }
    pub fn from_vec(mut items: Vec<T>, identity: T, aggregate: F) -> SegmentTree<T, F> {
        use self::segment_tree_internal::*;
        let node_count = items.len().saturating_sub(1);
        let mut heap = Vec::with_capacity(node_count + items.len());
        unsafe { heap.set_len(node_count); }
        heap.append(&mut items);
        for i in (0..node_count).rev() {
            heap[i] = aggregate(&heap[left_of(i)], &heap[right_of(i)]);
        }
        SegmentTree {
            heap: heap,
            identity: identity,
            aggregate: aggregate
        }
    }
    fn node_count(&self) -> usize {
        self.heap.len() / 2
    }
    pub fn len(&self) -> usize {
        self.heap.len() - self.node_count()
    }
    pub fn is_empty(&self) -> bool {
        self.len() == 0
    }
    pub fn items(&self) -> &[T] {
        &self.heap[self.node_count() .. self.node_count()+self.len()]
    }
    pub fn query(&self, range: std::ops::Range<usize>) -> Option<T> {
        if self.len() <= range.start {
            return None;
        }
        if self.len() < range.end {
            return None;
        }
        if range.start <= range.end {
            Some(self.aggregate_interval(
                self.node_count() + range.start, self.node_count() + range.end,
                self.identity.clone(), self.identity.clone()
            ))
        } else {
            None
        }
    }
    fn aggregate_interval(&self, mut heap_start: usize, mut heap_end: usize,
                          mut acc_left: T, mut acc_right: T) -> T {
        use self::segment_tree_internal::*;
        if heap_end == heap_start {
            (self.aggregate)(&acc_left, &acc_right)
        } else {
            if is_root_or_right(heap_start) {
                acc_left = (self.aggregate)(&acc_left, &self.heap[heap_start]);
                heap_start += 1;
            }
            if is_root_or_right(heap_end) {
                heap_end -= 1;
                acc_right = (self.aggregate)(&self.heap[heap_end], &acc_right);
            }
            self.aggregate_interval(
                parent_of(heap_start), parent_of(heap_end), acc_left, acc_right
            )
        }
    }
    pub fn get_mut(&mut self, index: usize) -> Option<SegmentTreeItemRef<T, F>> {
        if index < self.len() {
            let heap_index = self.node_count() + index;
            Some(SegmentTreeItemRef {
                tree: self,
                heap_index: heap_index
            })
        } else {
            None
        }
    }
    pub fn at(&mut self, index: usize) -> SegmentTreeItemRef<T, F> {
        self.get_mut(index).unwrap()
    }
    fn update_ancestors(&mut self, heap_index: usize) {
        use self::segment_tree_internal::*;
        if heap_index != 0 {
            let parent = parent_of(heap_index);
            let l = left_of(parent);
            let r = right_of(parent);
            self.heap[parent] = (self.aggregate)(&self.heap[l], &self.heap[r]);
            self.update_ancestors(parent);
        }
    }
}
pub struct SegmentTreeItemRef<'a, T: 'a + Clone, F: 'a + Fn(&T, &T) -> T> {
    tree: &'a mut SegmentTree<T, F>,
    heap_index: usize
}
impl<'a, T, F> std::ops::Deref for SegmentTreeItemRef<'a, T, F>
where
    T: Clone,
    F: Fn(&T, &T) -> T
{
    type Target = T;
    fn deref(&self) -> &T {
        &self.tree.heap[self.heap_index]
    }
}
impl<'a, T, F> std::ops::DerefMut for SegmentTreeItemRef<'a, T, F>
where
    T: Clone,
    F: Fn(&T, &T) -> T
{
    fn deref_mut(&mut self) -> &mut T {
        &mut self.tree.heap[self.heap_index]
    }
}
impl<'a, T, F> Drop for SegmentTreeItemRef<'a, T, F>
where
    T: Clone,
    F: Fn(&T, &T) -> T
{
    fn drop(&mut self) {
        self.tree.update_ancestors(self.heap_index);
    }
}
/*
pub fn range_sum_segment_tree<T>(len: usize) -> SegmentTree<T, impl Fn(&T, &T) -> T>
where
    T: Clone + Numeric
{
    SegmentTree::new(len, T::zero(), |x, y| x.clone() + y)
}
*/
pub trait IteratorExtForSegmentTree: Sized + Iterator
where
    Self::Item: Clone
{
    fn segment_tree<F>(self, identity: Self::Item, aggregate: F) -> SegmentTree<Self::Item, F>
    where
        F: Fn(&Self::Item, &Self::Item) -> Self::Item
    {
        SegmentTree::from_vec(self.collect(), identity, aggregate)
    }
}
impl<I: Iterator> IteratorExtForSegmentTree for I where <I as Iterator>::Item: Clone {}

// SNIPPET dbg
#[macro_export]
#[cfg(local)]
macro_rules! dbg {
    () => {
        {
            use std::io::{self, Write};
            writeln!(io::stderr(), "{}: dbg", line!()).unwrap();
        }
    };
    ($e: expr) => {
        {
            use std::io::{self, Write};
            let result = $e;
            writeln!(io::stderr(), "{}: {} = {:?}",
                     line!(), stringify!($e), result)
                .unwrap();
            result
        }
    }
}
#[macro_export]
#[cfg(not(local))]
macro_rules! dbg {
    () => {};
    ($e: expr) => {
        { $e }
    }
}

// END SNIPPETS

fn main() {
    read!();
    read!(s = String);
    let init: Vec<u32> = s.chars().map(|c| {
        let i = (c as u8 - 'a' as u8) as u32;
        1 << i
    }).collect();
    let mut chars = SegmentTree::from_vec(init, 0, |&a, &b| a|b);
    read!();
    readx_loop!(|q_type = u8, param1 = usize, param2 = String| {
        if q_type == 1 {
            let i = param1 - 1;
            let c = param2.chars().next().unwrap();
            let x = 1 << (c as u8 - 'a' as u8) as u32;
            *chars.at(i) = x;
        } else {
            let start = param1 - 1;
            let end: usize = param2.parse().unwrap();
            let x = chars.query(start..end).unwrap();
            println!("{}", x.count_ones());
        }
    });
}


Measured memory_bytes: 12024