//#pragma GCC optimize("O3")
//#pragma GCC optimize("Ofast")
//#pragma GCC optimize ("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
//#pragma optimize("", off)
//#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops")
#include <chrono>
#include <thread>
#include <iostream>
#include <string>
#include <vector>
#include <set>
#include <bitset>
#include <array>
#include <algorithm>
#include <queue>
#include <map>
#include <iterator>
#include <cstring>
#include <stdlib.h>
#include <ctime>
#include <csetjmp>
#include <unordered_set>
#include <complex>
#include <unordered_map>
#pragma warning( disable:4996 )
////// long aruthmetic
#include <stack>


#ifndef LINT
#define LINT

#include <random>
#include <iomanip>

namespace apa
{
    using namespace std;

    template <typename T>
    class ComparisonOperators
    {
        friend bool operator==(T const& lhs, T const& rhs)
        {
            return lhs.compare(rhs) == 0;
        }

        friend bool operator!=(T const& lhs, T const& rhs)
        {
            return lhs.compare(rhs) != 0;
        }

        friend bool operator<(T const& lhs, T const& rhs)
        {
            return lhs.compare(rhs) < 0;
        }

        friend bool operator>(T const& lhs, T const& rhs)
        {
            return rhs.compare(lhs) < 0;
        }

        friend bool operator<=(T const& lhs, T const& rhs)
        {
            bool result = lhs.compare(rhs) <= 0;
            return result;
        }

        friend bool operator>=(T const& lhs, T const& rhs)
        {
            return rhs.compare(lhs) <= 0;
        }
    };

    class lint : ComparisonOperators<lint>
    {
    public:
        explicit lint(std::string number);

        lint();

        lint(long long number);

        lint(int number);

        lint(double number);

        lint(vector<int> nums, bool is_neg);

        lint(const lint &obj);

        int get_length() const;

        bool is_negative_number() const;

        lint& operator+=(const lint& b);

        lint& operator-=(const lint& b);

        lint& operator*=(const lint& number2);

        lint& operator/=(const lint& b);

        explicit operator bool() const;

        explicit operator int();

        lint operator+() const;

        lint operator-() const;

        int operator[](size_t index) const;

        lint& operator=(const lint& other);

        lint& operator++();

        lint operator++(int);

        lint& operator--();

        lint operator--(int);

        bool cmp(lint const& rhs) const;

        int compare(lint const& rhs) const;

        bool is_zero() const;

        std::string to_string();

    private:
        bool is_negative;
        vector<int> numbers;

        lint abs(lint number) const;

        vector<int> reverse_numbers(vector<int> const& numbers) const;

        void make_equal_length(const lint& b, vector<int> & number1, vector<int> & number2) const;

        void string_to_vector(std::string const& number);

        void integer_to_vector(long long a);
    };

    lint abs(lint number);

    lint pow(lint a, int n);

    std::ostream& operator<<(std::ostream& os, const lint& obj);

    std::istream& operator>>(std::istream& is, lint& obj);

    lint operator+(const lint& lhs, const lint& rhs);

    lint operator-(const lint& lhs, const lint& rhs);

    lint operator*(const lint& lhs, const lint& rhs);

    lint operator/(const lint& lhs, const lint& rhs);
}

#endif /* LINT */
namespace apa
{
    lint::lint(std::string number)
    {
        string_to_vector(number);
    }

    lint::lint()
    {
        integer_to_vector(0);
    }

    lint::lint(long long number)
    {
        integer_to_vector(number);
    }

    lint::lint(int number)
    {
        integer_to_vector(static_cast<long long>(number));
    }

    lint::lint(double number)
    {
        std::string str = std::to_string(std::trunc(number));
        std::string result = str.substr(0, str.size() - 7);
        string_to_vector(result);
    }

    lint::lint(vector<int> nums, bool is_neg)
    {
        numbers = nums;
        is_negative = is_neg;
    }

    lint::lint(const lint &obj) {
        is_negative = obj.is_negative_number();

        for (int t : obj.numbers)
        {
            numbers.push_back(t);
        }
    }

    int lint::get_length() const
    {
        return numbers.size();
    }

    bool lint::is_negative_number() const
    {
        return is_negative;
    }

    lint& lint::operator+=(const lint& b)
    {
        if (!is_negative_number() && b.is_negative_number())
        {
            lint temp(b);
            temp = abs(temp);

            return operator-=(temp);
        }

        if (is_negative_number() && !b.is_negative_number())
        {
            lint temp_this = lint(*this);
            temp_this.is_negative = false;

            lint temp = lint(b);
            temp -= temp_this;
            *this = temp;

            return *this;
        }

        vector<int> number1;
        vector<int> number2;

        make_equal_length(b, number1, number2);

        vector<int> result;
        int rest = 0;

        for (int i = number1.size() - 1; i >= 0; --i)
        {
            int sum = number1[i] + number2[i] + rest;

            if (sum > 9)
            {
                rest = 1;
                sum -= 10;
            }
            else
            {
                rest = 0;
            }

            result.push_back(sum);
        }

        if (rest > 0)
        {
            result.push_back(rest);
        }

        vector<int> reverse_result = reverse_numbers(result);

        (*this).numbers = reverse_result;

        return *this;
    }

    lint& lint::operator-=(const lint& b)
    {
        if (!is_negative_number() && b.is_negative_number())
        {
            return (*this).operator+=(abs(b));
        }

        if (is_negative_number() && !b.is_negative_number())
        {
            lint temp(b);
            temp.is_negative = true;
            return (*this).operator+=(temp);
        }

        vector<int> number1;
        vector<int> number2;

        make_equal_length(b, number1, number2);

        int is_number1_more_than_number2 = 0;

        for (unsigned int i = 0; i < number1.size(); ++i)
        {
            if (number1[i] > number2[i])
            {
                is_number1_more_than_number2 = 1;
                break;
            }
            else if (number1[i] < number2[i])
            {
                is_number1_more_than_number2 = 2;
                break;
            }
        }

        if (is_number1_more_than_number2 == 0)
        {
            vector<int> t;
            t.push_back(0);
            numbers = t;
            return *this;
        }

        vector<int> result;

        if (is_number1_more_than_number2 == 1)
        {
            for (int i = number1.size() - 1; i >= 0; --i)
            {
                if (number1[i] < number2[i])
                {
                    number1[i] += 10;
                    number1[i - 1] -= 1;
                }

                int r = number1[i] - number2[i];

                result.push_back(r);
            }
        }
        else if (is_number1_more_than_number2 == 2)
        {
            for (int i = number2.size() - 1; i >= 0; --i)
            {
                if (number2[i] < number1[i])
                {
                    number2[i] += 10;
                    number2[i - 1] -= 1;
                }

                int r = number2[i] - number1[i];

                result.push_back(r);
            }
        }

        bool can_copy = false;
        vector<int> result_without_zero;

        for (int i = result.size() - 1; i >= 0; --i)
        {
            if (result[i] != 0)
            {
                can_copy = true;
            }

            if (can_copy)
            {
                result_without_zero.push_back(result[i]);
            }
        }

        (*this).numbers = result_without_zero;

        if (!is_negative_number() && !b.is_negative_number())
        {
            if (is_number1_more_than_number2 == 2)
            {
                is_negative = true;
            }
        }

        if (is_negative_number() && b.is_negative_number())
        {
            if (is_number1_more_than_number2 == 2)
            {
                is_negative = false;
            }
        }

        return *this;
    }

    lint& lint::operator*=(const lint& number2)
    {
        vector<int> a = reverse_numbers(numbers);
        vector<int> b = reverse_numbers(number2.numbers);

        vector<int> c(a.size() + b.size(), 0);

        for (size_t i = 0; i < a.size(); ++i)
        {
            int carry = 0;

            for (unsigned int j = 0; j < b.size() || carry; ++j)
            {
                long long cur = c[i + j] + a[i] * 1ll * (j < b.size() ? b[j] : 0) + carry;

                c[i + j] = int(cur % 10);
                carry = int(cur / 10);
            }
        }

        while (c.size() > 1 && c.back() == 0)
        {
            c.pop_back();
        }

        vector<int> result = reverse_numbers(c);

        numbers = result;

        if (is_negative_number() && !number2.is_negative_number())
        {
            is_negative = true;
        }
        else if (!is_negative_number() && number2.is_negative_number())
        {
            is_negative = true;
        }
        else
        {
            is_negative = false;
        }

        return *this;
    }

    lint& lint::operator/=(const lint& number2)
    {
        if (number2.is_zero())
        {
            int d = 4 - 4;
            int a = 4 / d;
            numbers.push_back(a);
        }

        if (is_zero())
        {
            vector<int> temp;
            temp.push_back(0);
            numbers = temp;
            is_negative = false;
            return *this;
        }

        bool second_number_more_then_first_number = abs(*this).cmp(abs(number2));

        if (second_number_more_then_first_number)
        {
            vector<int> temp;
            temp.push_back(0);
            numbers = temp;
            is_negative = false;
            return *this;
        }

        vector<int> res;
        for (int i = (*this).get_length() - 1; i >= 0; --i)
        {
            res.push_back(0);
        }

        lint current_value(0);
        for (int i = 0; i < (*this).get_length(); ++i)
        {
            current_value = current_value * 10;
            current_value.numbers[current_value.get_length() - 1] = (*this).numbers[i];

            int x = 0;
            int left_index = 0;
            int right_index = 10;

            while (left_index <= right_index)
            {
                int middle = (left_index + right_index) >> 1;

                lint cur = abs(number2) * middle;

                if (abs(cur) <= abs(current_value))
                {
                    x = middle;
                    left_index = middle + 1;
                }
                else
                {
                    right_index = middle - 1;
                }
            }

            res[i] = x;
            current_value = current_value - abs(number2) * x;
        }

        res = reverse_numbers(res);

        while (res.size() > 1 && res.back() == 0)
        {
            res.pop_back();
        }

        res = reverse_numbers(res);

        numbers = res;

        if (is_negative_number() && !number2.is_negative_number())
        {
            is_negative = true;
        }
        else if (!is_negative_number() && number2.is_negative_number())
        {
            is_negative = true;
        }
        else
        {
            is_negative = false;
        }

        return *this;
    }

    lint::operator bool() const
    {
        return !is_zero();
    }

    lint::operator int()
    {
        return std::stoi((*this).to_string());
    }

    lint lint::operator+() const
    {
        lint temp(*this);
        return temp;
    }

    lint lint::operator-() const
    {
        lint temp(*this);

        if (is_negative_number())
        {
            temp.is_negative = false;
        }
        else
        {
            temp.is_negative = true;
        }

        return temp;
    }

    int lint::operator[](size_t index) const
    {
        return numbers[index];
    }

    lint& lint::operator=(const lint& other)
    {
        if (this != &other)
        {
            numbers = other.numbers;
            is_negative = other.is_negative_number();
        }
        return *this;
    }

    lint& lint::operator++()
    {
        lint one(1);
        (*this) += one;
        return *this;
    }

    lint lint::operator++(int) {
        lint tmp(*this);
        operator++();
        return tmp;
    }

    lint& lint::operator--()
    {
        lint one(1);
        (*this) -= one;
        return *this;
    }

    lint lint::operator--(int) {
        lint tmp(*this);
        operator--();
        return tmp;
    }

    bool lint::cmp(lint const& rhs) const
    {
        if (is_negative_number() && !rhs.is_negative_number())
        {
            return true;
        }

        if (!is_negative_number() && rhs.is_negative_number())
        {
            return false;
        }

        if (get_length() < rhs.get_length())
        {
            return true;
        }

        if (get_length() > rhs.get_length())
        {
            return false;
        }

        for (int i = 0; i < get_length(); ++i)
        {
            if (numbers[i] < rhs[i])
            {
                if (is_negative_number())
                {
                    return false;
                }
                return true;
            }
            else if (numbers[i] > rhs[i])
            {
                if (is_negative_number())
                {
                    return true;
                }
                return false;
            }
        }

        return false;
    }

    int lint::compare(lint const& rhs) const
    {
        if ((*this).cmp(rhs))
        {
            return -1;
        }
        else if (rhs.cmp(*this))
        {
            return 1;
        }
        else
        {
            return 0;
        }
    }

    lint lint::abs(lint number) const
    {
        number.is_negative = false;
        return number;
    }

    bool lint::is_zero() const
    {
        if (numbers.size() == 1 && numbers[0] == 0)
        {
            return true;
        }

        return false;
    }

    std::string int_to_string(int i)
    {
        std::stringstream ss;
        std::string s;
        ss << i;
        s = ss.str();

        return s;
    }

    std::string lint::to_string()
    {
        std::string result = "";

        if (is_negative_number() && !is_zero())
        {
            result += "-";
        }

        for (int i = 0; i < get_length(); ++i)
        {
            int a = (*this)[i];
            result += int_to_string(a);
        }

        return result;
    }

    vector<int> lint::reverse_numbers(vector<int> const& numbers) const
    {
        vector<int> reverse_result;

        for (int i = numbers.size() - 1; i >= 0; --i)
        {
            reverse_result.push_back(numbers[i]);
        }

        return reverse_result;
    }

    void lint::make_equal_length(lint const& b, vector<int>& number1, vector<int>& number2) const
    {
        int diff_length = get_length() - b.get_length();

        if (diff_length > 0)
        {
            number1 = (*this).numbers;

            for (int i = 0; i < diff_length; ++i)
            {
                number2.push_back(0);
            }

            for (int i = 0; i < b.get_length(); ++i)
            {
                number2.push_back(b[i]);
            }
        }
        else if (diff_length < 0)
        {
            for (int i = 0; i < b.get_length(); ++i)
            {
                number2.push_back(b[i]);
            }

            for (int i = 0; i < (diff_length * (-1)); ++i)
            {
                number1.push_back(0);
            }

            for (int i = 0; i < get_length(); ++i)
            {
                number1.push_back((*this)[i]);
            }
        }
        else
        {
            for (int i = 0; i < b.get_length(); ++i)
            {
                number1.push_back((*this)[i]);
                number2.push_back(b[i]);
            }
        }
    }

    void lint::string_to_vector(std::string const& number)
    {
        unsigned int from = 0;

        if (number[0] == '-')
        {
            is_negative = true;
            from = 1;
        }
        else
        {
            is_negative = false;
        }

        for (unsigned int i = from; i < number.length(); ++i)
        {
            int ia = number[i] - '0';
            numbers.push_back(ia);
        }
    }

    void lint::integer_to_vector(long long a)
    {
        if (a < 0)
        {
            is_negative = true;
            a = (-1) * a;
        }
        else
        {
            is_negative = false;
        }

        if (a == 0)
        {
            numbers.push_back(0);
        }

        vector<int> temp;

        while (a)
        {
            int x = a % 10;
            a /= 10;
            temp.push_back(x);
        }

        for (int i = temp.size() - 1; i >= 0; --i)
        {
            numbers.push_back(temp[i]);
        }
    }

    lint abs(lint number)
    {
        lint n(number);
        lint zero(0);

        bool is_less = n.cmp(zero);

        if (is_less)
        {
            n *= lint(-1);
        }
        return n;
    }

    lint pow(lint a, int n) {
        lint res(1);

        while (n)
        {
            if (n & 1)
            {
                res *= a;
            }

            a *= a;
            n >>= 1;
        }

        return res;
    }

    std::ostream& operator<<(std::ostream& os, const lint& obj)
    {
        if (obj.is_negative_number())
        {
            os << "-";
        }

        for (int i = 0; i < obj.get_length(); ++i)
        {
            os << obj[i];
        }

        return os;
    }

    std::istream& operator>>(std::istream& is, lint& obj)
    {
        bool is_lead_zeros = true;
        bool is_negative = false;
        vector<int> numbers;

        while (is.good())
        {
            char c = static_cast<char>(is.get());
            int ic = c - '0';

            if (c == '\n')
            {
                break;
            }

            if (c == EOF)
            {
                break;
            }

            if (c == '\0')
            {
                break;
            }

            if (is.good())
            {
                if (c == '-')
                {
                    is_negative = true;
                }
                else if (c == '+')
                {
                    is_negative = false;
                }
                else if (ic == 0 && is_lead_zeros)
                {

                }
                else
                {
                    numbers.push_back(ic);
                    is_lead_zeros = false;
                }
            }
        }

        lint temp(numbers, is_negative);
        obj = temp;

        return is;
    }

    lint operator+(const lint& lhs, const lint& rhs)
    {
        lint temp(lhs);

        return temp += rhs;
    }

    lint operator-(const lint& lhs, const lint& rhs)
    {
        lint temp(lhs);

        return temp -= rhs;
    }

    lint operator*(const lint& lhs, const lint& rhs)
    {
        lint temp(lhs);

        return temp *= rhs;
    }

    lint operator/(const lint& lhs, const lint& rhs)
    {
        lint temp(lhs);

        return temp /= rhs;
    }
}
////////
#define var auto
using namespace std;
//////////////////////////////////////////

/////////////////////////////////////////
const long long inf = 2000000000;
#define MEM(a,b) memset(a,b,sizeof(a))
#define iOS ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);

#define lol long long

template <typename t>
t gcd(t a, t b) { return (!b) ? a : gcd(b, a%b); }
template <typename t>
long long  pow(t a, t b) {
    if (b == 0)return 1;
    long  long cur = pow(a, b / 2);
    if (b % 2 == 0)return (1ll*cur * cur) % 1000000007;
    else return (1ll*cur * cur * a )% 1000000007;
}
template <typename t>
bool isOk(t x, t y, t boundX, t boundY) {
    return ((x >= 0) && (y >= 0) && (x < boundX) && (y < boundY));
}


double square(vector<pair<double, double>> nodes)
{
    double area = 0;
    int numPoints = nodes.size();
    int j = numPoints - 1;  // The last vertex is the 'previous' one to the first

    for (int i = 0; i<numPoints; i++)
    {
        area = area + (nodes[j].first + nodes[i].first) * (nodes[j].second - nodes[i].second);
        j = i;  //j is previous vertex to i
    }
    return area / 2;
}


struct PointF
{

    double X;
    double Y;
    PointF(double x, double y)
    {
        X = x; Y = y;
    }

};
//int FindLineCircleIntersections(
//	double cx, double cy, double radius,
//	PointF point1, PointF point2,
//	PointF &intersection1, PointF &intersection2)
//{
//	double dx, dy, A, B, C, det, t;
//
//	dx = point2.X - point1.X;
//	dy = point2.Y - point1.Y;
//
//	A = dx * dx + dy * dy;
//	B = 2 * (dx * (point1.X - cx) + dy * (point1.Y - cy));
//	C = (point1.X - cx) * (point1.X - cx) +
//		(point1.Y - cy) * (point1.Y - cy) -
//		radius * radius;
//
//	det = B * B - 4 * A * C;
//	if ((A <= 0.0000001) || (det < 0))
//	{
//		// No real solutions.
//		intersection1 = PointF(inf, inf);
//		intersection2 = PointF(inf, inf);
//		return 0;
//	}
//	else if (det == 0)
//	{
//		// One solution.
//		t = -B / (2 * A);
//		intersection1 =
//			PointF(point1.X + t * dx, point1.Y + t * dy);
//		intersection2 = PointF(inf, inf);
//		return 1;
//	}
//	else
//	{
//		// Two solutions.
//		t = (double)((-B + sqrt(det)) / (2 * A));
//		intersection1 =
//			PointF(point1.X + t * dx, point1.Y + t * dy);
//		t = (double)((-B - sqrt(det)) / (2 * A));
//		intersection2 =
//			PointF(point1.X + t * dx, point1.Y + t * dy);
//		return 2;
//	}
//}
//set <int > seta = { 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368 };


double distance(double x1, double y1, double x2, double y2)
{
    return sqrt((x2 - x1)*(x2 - x1) + (y2 - y1)*(y2 - y1));
}

//unordered_set<int> primes[2000000];
//bool er[2000005];
//void primeFactors(int n, const int& index)
//{
//
//	// Print the number of 2s that divide n
//	while (n % 2 == 0)
//	{
//		n = n / 2;
//		primes[index].insert(2);
//	}
//
//	// n must be odd at this point.  So we can skip
//	// one element (Note i = i +2)
//	for (int i = 3; i*i <= n+1; i = i + 2)
//	{
//		// While i divides n, print i and divide n
//		while (n%i == 0)
//		{
//
//			primes[index].insert(i);
//			n = n / i;
//		}
//	}
//
//	// This condition is to handle the case when n
//	// is a prime number greater than 2
//	if (n > 2)
//		primes[index].insert(n);
//}

struct custom_hash {
    static uint64_t splitmix64(uint64_t x) {
        // http://xorshift.di.unimi.it/splitmix64.c
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};

class FenwickTree {
public:
    void updateBinaryIndexedTree(vector<int>& binaryIndexedTree, int val, int index) {
        while (index < binaryIndexedTree.size()) {
            binaryIndexedTree[index] += val;
            index = getNext(index);
        }
    }

    int getSum(vector <int>& binaryIndexedTree, int index) {
        int sum = 0;
        while (index >= 0) {
            sum += binaryIndexedTree[index];
            index = getParent(index);
        }
        return sum;
    }

    int getParent(int i) {
        return  (i & (i + 1)) - 1;
    }

    int getNext(int i) {
        return i | (i + 1);
    }
    static void test() {
        vector<int> input = { 1,2,3,4,5,6,7 };
        FenwickTree ft;
        vector <int> binaryIndexedTree(input.size() + 1, 0);

        for (int i = 0; i< input.size(); ++i)
        {
            ft.updateBinaryIndexedTree(binaryIndexedTree, input[i], i);
        }

        cout << (bool)(1 == (int)ft.getSum(binaryIndexedTree, 0));
        cout << (bool)(3 == (int)ft.getSum(binaryIndexedTree, 1));
        cout << (bool)(6 == (int)ft.getSum(binaryIndexedTree, 2));
        cout << (bool)(10 == (int)ft.getSum(binaryIndexedTree, 3));
        cout << (bool)(15 == (int)ft.getSum(binaryIndexedTree, 4));
        cout << (bool)(21 == (int)ft.getSum(binaryIndexedTree, 5));
        cout << (bool)(28 == (int)ft.getSum(binaryIndexedTree, 6));
    }
};
struct mp {
    mp(int _x, int _y) {
        x = _x;
        y = _y;
    }
    mp() {};
    long long x, y;
    friend bool operator < (mp rhs, mp another) {
        return (long long)(rhs.x + (long long)rhs.y * 5322) <  (long long)(another.x + (long long)another.y * 5322);
    }
    friend bool operator == (mp rhs, mp another) {
        return (long long)(rhs.x + (long long)rhs.y * 5322) == (long long)(another.x + (long long)another.y * 5322);
    }
};

long long bits[] = { 1
        ,	2
        ,	4
        ,	8
        ,	16
        ,	32
        ,	64
        ,	128
        ,	256
        ,	512
        ,	1024
        ,	2048
        ,	4096
        ,	8192
        ,	16384
        ,	32768
        ,	65536
        ,	131072
        ,	262144
        ,	524288
        ,	1048576
        ,	2097152
        ,	4194304
        ,	8388608
        ,   16777216
        ,	33554432
        ,	67108864
        ,	134217728
        ,	268435456
        ,	536870912
        ,	1073741824
        ,	2147483648 };


lol merged (lol a , lol b) {
    return a+ b;
}
struct SegTree {
    vector <lol> tree;
    vector <lol> lazy;
    int upbound;
    SegTree (int n ){
        int pow2 = 1;
        while (pow2 < n){
            pow2 = (pow2<<1);
        }
        tree.resize(pow2*2 -1);
        for (int i = 0 ;i < tree.size();  ++ i){
            tree[i] = 0;
        }
        lazy.resize(pow2*2 -1);
        upbound = n-1;
    }
public:

    void create(vector<lol>& input) {
        create(input, 0, input.size()-1, 0);
    }
    lol query(int l, int r){
        return query(l,r,0,upbound,0);
    }
    void update(int index, int delta){
        updateSegmentTree(index, delta, 0, upbound,0);
    }
    void updateRange(int l, int r, int delta) {
        updateRange(l,r,delta,0,upbound,0);
    }
    void updateLazy(int l, int r, int delta ) {
        updateLazy(l,r,delta, 0,upbound, 0);
    }
    lol queryLazy (int l, int r) {
        return queryLazy(l,r,0,upbound,0);
    }
private:

    void create (vector<lol>& input, int l, int r, int pos) {
        if (l == r) {
            tree[pos] = input[l];
            return;
        }
        int mid = (l + r) /2;
        create(input, l , mid, 2*pos+1);
        create(input, mid + 1 , r , 2*pos+2);
        tree[pos] = merged (tree[2*pos + 1], tree[2 * pos+2]);
    }
    lol query(int ql, int qr, int l, int r, int pos) {
        if (ql <= l && qr >= r)
            return tree[pos];
        if (ql > r || qr < l) {
            return 0;
        }
        int mid = (l + r)/2;
        return merged (query(ql, qr, l, mid, pos*2 +1), query(ql, qr, mid + 1, r, pos*2 + 2));
    }

    void updateSegmentTree(int index, int delta, int low, int high, int pos){

        //if index to be updated is less than low or higher than high just return.
        if(index < low || index > high){
            return;
        }

        //if low and high become equal, then index will be also equal to them and update
        //that value in segment tree at pos
        if(low == high){
            tree[pos] += delta;
            return;
        }
        //otherwise keep going left and right to find index to be updated
        //and then update current tree position if min of left or right has
        //changed.
        int mid = (low + high)/2;
        updateSegmentTree( index, delta, low, mid, 2 * pos + 1);
        updateSegmentTree( index, delta, mid + 1, high, 2 * pos + 2);
        tree[pos] = merged(tree[2*pos+1], tree[2*pos + 2]);
    }

    void updateRange( int startRange, int endRange, int delta, int low, int high, int pos) {
        if(low > high || startRange > high || endRange < low ) {
            return;
        }

        if(low == high) {
            tree[pos] += delta;
            return;
        }

        int middle = (low + high)/2;
        updateRange( startRange, endRange, delta, low, middle, 2 * pos + 1);
        updateRange( startRange, endRange, delta, middle + 1, high, 2 * pos + 2);
        tree[pos] = merged(tree[2*pos+1], tree[2*pos+2]);
    }

    void updateLazy( int startRange, int endRange, int delta, int low, int high, int pos) {
        if (low > high) {
            return;
        }

        //make sure all propagation is done at pos. If not update tree
        //at pos and mark its children for lazy propagation.
        if (lazy[pos] != 0) {
            tree[pos] += lazy[pos];
            if (low != high) { //not a leaf node
                lazy[2 * pos + 1] += lazy[pos];
                lazy[2 * pos + 2] += lazy[pos];
            }
            lazy[pos] = 0;
        }

        //no overlap condition
        if (startRange > high || endRange < low) {
            return;
        }

        //total overlap condition
        if (startRange <= low && endRange >= high) {
            tree[pos] += delta;
            if (low != high) {
                lazy[2 * pos + 1] += delta;
                lazy[2 * pos + 2] += delta;
            }
            return;
        }
        int mid = (low + high)/2;
        updateLazy(  startRange, endRange,
                     delta, low, mid, 2*pos+1);
        updateLazy( startRange, endRange,
                    delta, mid+1, high, 2*pos+2);
        tree[pos] = merged(tree[2*pos + 1], tree[2*pos + 2]);
    }

    lol queryLazy( int qlow, int qhigh, int low, int high, int pos) {

        if(low > high) {
            return 0;
        }

        //make sure all propagation is done at pos. If not update tree
        //at pos and mark its children for lazy propagation.
        if (lazy[pos] != 0) {
            tree[pos] += lazy[pos];
            if (low != high) { //not a leaf node
                lazy[2 * pos + 1] += lazy[pos];
                lazy[2 * pos + 2] += lazy[pos];
            }
            lazy[pos] = 0;
        }

        //no overlap
        if(qlow > high || qhigh < low){
            return 0;
        }

        //total overlap
        if(qlow <= low && qhigh >= high){
            return tree[pos];
        }

        //partial overlap
        int mid = (low+high)/2;
        return merged(queryLazy( qlow, qhigh, low, mid, 2 * pos + 1),
                      queryLazy( qlow, qhigh, mid + 1, high, 2 * pos + 2));

    }
public :
    static void test () {
        vector<lol> input =  {0,3,4,2,1,6,-1};
        SegTree tr(input.size());
        tr.create(input);
        cout << (bool)(0 == tr.query(0, 3)) << endl;
        cout << (bool)(1 == tr.query(1, 5)) << endl;
        cout << (bool)(-1 == tr.query(1, 6)) << endl;
        tr.update(2,1);
        cout << (bool)(2 == tr.query(1 , 3 )) << endl;
        tr.updateRange(3,5,-2);
        cout << (bool)(-1 == tr.query(5, 6)) << endl;
        cout << (bool)(0 == tr.query(0, 3)) << endl;
        vector<lol> input1 = {-1,2,4,1,7,1,3,2};
        SegTree tr1(input1.size());
        tr1.create(input1);
        tr1.updateLazy(0,3,1);
        tr1.updateLazy(0,0,2);
        cout << (bool)( 1 == tr1.queryLazy(3,5) ) <<endl;
    }
};
//unique vector
//sort(list.begin(), list.end());
//list.resize( unique(list.begin(), list.end()) - list.begin() );

void solve () {
    int n ;
    cin >> n;
    vector<int> v;
    lol sum = 0;

    int mx = 0;
    for (int i =0 ;i < n; ++i) {
        int t;
        cin >> t;
        mx = max (mx, t);
        sum += t;
    }
    cout << sum - mx/2 << endl;

}


int32_t  main() {
    iOS
    // srand(time(0));

#ifdef areubreathing
    // std::freopen("input.in","r",stdin);
    // std::freopen("output2.txt","w",stdout);
    // std::freopen("output.txt","r",stdin);
    double beg=clock();
#endif
    int n = 1;
    //cin >> n;
    for (int i = 0; i < n; ++i) {
        solve();
    }
#ifdef areubreathing
    double end=clock();
    fprintf(stderr,"*** Total time = %.1f ***\n",(end-beg)/CLOCKS_PER_SEC);
#endif
    return 0;
}

Measured memory_bytes: 256