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use std::cmp;
const NUM: usize = 1 << 20;
const INF: i64 = 1 << 60;

pub struct RangeAddSegmentTree {
    seg_min: Vec<i64>,
    seg_max: Vec<i64>,
    seg_add: Vec<i64>,
}

impl RangeAddSegmentTree {
    pub fn new() -> Self {
        RangeAddSegmentTree {
            seg_min: vec![INF; NUM * 2],
            seg_max: vec![-INF; NUM * 2],
            seg_add: vec![0; NUM * 2],
        }
    }

    /// add to [a, b)
    pub fn add(&mut self, a: usize, b: usize, value: i64) {
        self.add_to_range(a, b, value, 0, 0, NUM);
    }

    fn add_to_range(
        &mut self,
        a: usize,
        b: usize,
        value: i64,
        k: usize,
        left: usize,
        right: usize,
    ) {
        if b <= left || right <= a {
            return;
        }
        if a <= left && right <= b {
            let mut k = k;
            self.seg_add[k] += value;
            while k > 0 {
                k = (k - 1) / 2;
                self.seg_min[k] = cmp::min(
                    self.seg_min[k * 2 + 1] + self.seg_add[k * 2 + 1],
                    self.seg_min[k * 2 + 2] + self.seg_add[k * 2 + 2],
                );
                self.seg_max[k] = cmp::max(
                    self.seg_max[k * 2 + 1] + self.seg_add[k * 2 + 1],
                    self.seg_max[k * 2 + 2] + self.seg_add[k * 2 + 2],
                );
            }
        } else {
            self.add_to_range(a, b, value, k * 2 + 1, left, (left + right) / 2);
            self.add_to_range(a, b, value, k * 2 + 2, (left + right) / 2, right);
        }
    }

    pub fn update(&mut self, pos: usize, value: i64) {
        let mut k = pos + NUM - 1;
        self.seg_min[k] = value;
        self.seg_max[k] = value;
        while k > 0 {
            k = (k - 1) / 2;
            self.seg_min[k] = cmp::min(self.seg_min[k * 2 + 1], self.seg_min[k * 2 + 2]);
            self.seg_max[k] = cmp::max(self.seg_max[k * 2 + 1], self.seg_max[k * 2 + 2]);
        }
    }

    pub fn get_min(&self, a: usize, b: usize) -> i64 {
        self.get_min_range(a, b, 0, 0, NUM)
    }

    fn get_min_range(&self, a: usize, b: usize, k: usize, left: usize, right: usize) -> i64 {
        if b <= left || right <= a {
            INF
        } else if a <= left && right <= b {
            self.seg_min[k] + self.seg_add[k]
        } else {
            let x = self.get_min_range(a, b, k * 2 + 1, left, (left + right) / 2);
            let y = self.get_min_range(a, b, k * 2 + 2, (left + right) / 2, right);
            cmp::min(x, y) + self.seg_add[k]
        }
    }

    pub fn get_max(&self, a: usize, b: usize) -> i64 {
        self.get_max_range(a, b, 0, 0, NUM)
    }

    fn get_max_range(&self, a: usize, b: usize, k: usize, left: usize, right: usize) -> i64 {
        if b <= left || right <= a {
            -INF
        } else if a <= left && right <= b {
            self.seg_max[k] + self.seg_add[k]
        } else {
            let x = self.get_max_range(a, b, k * 2 + 1, left, (left + right) / 2);
            let y = self.get_max_range(a, b, k * 2 + 2, (left + right) / 2, right);
            cmp::max(x, y) + self.seg_add[k]
        }
    }
}

#[cfg(test)]
mod test {
    use super::*;
    extern crate rand;
    use self::rand::Rng;

    #[test]
    fn random_add() {
        let n = 30;
        let mut array = vec![0; n];
        let mut seg = RangeAddSegmentTree::new();
        for i in 0..n {
            seg.update(i, 0);
        }

        for l in 0..n {
            for r in (l + 1)..n {
                let value = rand::thread_rng().gen::<i16>() as i64;
                seg.add(l, r, value);

                for i in l..r {
                    array[i] += value;
                }

                for l in 0..n {
                    for r in (l + 1)..n {
                        let mut min = INF;
                        let mut max = -INF;
                        for i in l..r {
                            min = cmp::min(min, array[i]);
                            max = cmp::max(max, array[i]);
                        }

                        assert_eq!(seg.get_min(l, r), min);
                        assert_eq!(seg.get_max(l, r), max);
                    }
                }
            }
        }
    }
}