new_template

#include <cstdio>
#include <cmath>
#include <cstring>
#include <cctype>
#include <cstdlib>
#include <climits>
#include <ctime>
#include <cassert>
#include <istream>
#include <ostream>
#include <iostream>
#include <iomanip>
#include <algorithm>
#include <vector>
#include <string>
#include <numeric>
#include <fstream>
#include <sstream>
#include <map>
#include <set>
#include <list>
#include <stack>
#include <queue>
#include <deque>
#include <complex>
#include <limits>
#include <bitset>
#include <iterator>
#include <utility>
#include <functional>
#include <tr1/unordered_map>

#define eps (1e-9)
#define vinf (1 << 28)
#define nvinf (-(1 << 28))
#define inf ((~0U) >> (1))
#define pi (2.0 * acos(0.0))
#define d_zero(x) (abs(x) < eps)
#define lowbit(x) ((x) & (-(x)))
#define sine(x) (sin(radians(x)))
#define cosine(x) (cos(radians(x)))
#define setbit(x, i) (x |= (1 << i))
#define tangent(x) (tan(radians(x)))
#define arcsine(x) (degrees((asin(x))))
#define resetbit(x, i) (x &= (~(1 << i)))
#define arccosine(x) (degrees((acos(x))))
#define arctangent(x) (degrees((atan(x))))
#define d_equals(a, b) (d_zero((a) - (b)))
#define getbit(x, i) (x & (1 << i) ? 1 : 0)
#define clr(ar) (memset(ar, 0, sizeof(ar)))
#define radians(x) (((1.0 * x * pi) / 180.0))
#define degrees(x) (((x * 180.0) / (1.0 * pi)))
#define read() (freopen("lol.txt", "r+", stdin))
#define out() (freopen("out.txt", "w+", stdout))
#define write() (freopen("lol.txt", "w+", stdout))
#define d_lesser(a, b) (!d_equals(a, b) && (a) < (b))
#define d_greater(a, b) (!d_equals(a, b) && (a) > (b))
#define dbg(x) (std::cout << #x << " = " << x << endl)
#define flipbit(x, i) (getbit(x, i) ? (resetbit(x, i)) : (setbit(x, i)))
#define twopow(x) ((((x & (x - 1)) == 0) && (x != 0)) ? (true) : (false))
#define mod(n, m) ((n >= 0) ? (n % m) : ((abs(n) % m) == 0) ? 0 : (m - (abs(n) % m)))

using namespace std;