#define NDEBUG

#include <stdlib.h>
#include <vector>
#include <iostream>
#include <limits>

template <typename T = long> class SegmentTree;
template <typename T = long> class SumSegmentTree;
template <typename T = long> class MinSegmentTree;
template <typename T = long> class MaxSegmentTree;
template <typename T = long> class DifferenceSegmentTree;

template <typename T>
class SumSegmentTree : public SegmentTree<T> {
    virtual T cmp (T a, T b) override {
        return a + b;
    }

    public:
    SumSegmentTree(size_t N) : SegmentTree<T>(N, 0) {};
};

template <typename T>
class MinSegmentTree : public SegmentTree<T> {
    virtual T cmp (T a, T b) override {
        return (a < b) ? a : b;
    }

    public:
    MinSegmentTree(size_t N) : SegmentTree<T>(N, std::numeric_limits<T>::max()) {};
};

template <typename T>
class MaxSegmentTree : public SegmentTree<T> {
    virtual T cmp (T a, T b) override {
        return (a > b) ? a : b;
    }

    public:
    MaxSegmentTree(size_t N) : SegmentTree<T>(N, std::numeric_limits<T>::min()) {};
};

template <typename T>
class DifferenceSegmentTree : public SegmentTree<T> {
    virtual T cmp (T a, T b) override {
        return a+b;
    }

    public:
    virtual void add(size_t i, T val) override {
        this->set(i, this->get(i) + val);
        if (i != this->N-1)
            this->set(i+1, this->get(i+1) - val);
    }

    void add_range(size_t i, size_t j, T val) {
        this->set(i, this->get(i) + val);
        if (j+1 != this->N)
            this->set(j+1, this->get(j+1)-val);
    }

    DifferenceSegmentTree(size_t N) : SegmentTree<T>(N, 0) {};
};

template <typename T>
class SegmentTree {
    const T unit;
    virtual T cmp (T a, T b) = 0;
    std::vector<T> arr;

    public:
    size_t N;

    void print() {
        size_t newline = 2;
        for (size_t i = 1; i < 2*N; i++) {
            std::cout << arr[i] << " ";
            if (i == newline-1) {
                std::cout << std::endl;
                newline *= 2;
            }
        }
    }

    SegmentTree(size_t N, T unit) : unit(unit) {
        this->N = N;
        // Initialize the array to the size of the smallest power of two greater than N
        size_t exp = 0;
        while (N != 0) {
            N = N >> 1;
            exp++;
        }
        if ((size_t)(1 << (exp-1)) == this->N)
            arr = std::vector<T>(this->N*2, unit);
        else
            arr = std::vector<T>(1 << (exp+1), unit);
    }

    T get(size_t i) {
#ifndef NDEBUG
        if (i >= N)
            std::cerr << "Tried accessing index " << i << " out of " << N-1 << " (remember, 0-indexing)"  << std::endl;
#endif
        return arr[i+N];
    }
    /* T operator[](size_t i) { get(i); }; */

    virtual void set(size_t i, T val) {
        update_field(i, val);
    }

    void update_field(size_t i, T val) {
#ifndef NDEBUG
        if (i >= N)
            std::cerr << "Tried updating index " << i << " out of " << N-1 << " (remember, 0-indexing)" << std::endl;
#endif
        i += N; // Put the index at the leaf nodes/original array
        arr[i] = val;
        for (i /= 2; i >= 1; i /= 2)
            arr[i] = cmp(arr[i*2], arr[i*2+1]);
    }

    virtual void add(size_t i, T val) {
        set(i, val + get(i));
    }

    T query(size_t a, size_t b) {
#ifndef NDEBUG
        if (a > N || b > N || a > b)
            std::cerr << "Tried querying the range: [" << a << ", " << b << "]" << " of max index " << N-1 << std::endl;
#endif
        a += N; b += N;
        size_t val = unit;
        while (a <= b) {
            if (a % 2 == 1) val = cmp(val, arr[a++]);
            if (b % 2 == 0) val = cmp(val, arr[b--]);
            a /= 2; b /= 2;
        }
        return val;
    }
};