#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pill = pair<int, ll>;
using plli = pair<ll, int>;
using pdd = pair<double, double>;
using pld = pair<ld, ld>;
constexpr const char nl = '\n', sp = ' ';
constexpr const int INT_INF = 0x3f3f3f3f;
constexpr const ll LL_INF = 0x3f3f3f3f3f3f3f3f;
constexpr const double D_INF = numeric_limits<double>::infinity();
constexpr const ld LD_INF = numeric_limits<ld>::infinity();
constexpr const double EPS = 1e-9;
template <typename T>
bool feq(const T& x, const T& y) {
  return abs(x - y) <= EPS;
}
template <typename T>
bool flt(const T& x, const T& y) {
  return x < y - EPS;
}
template <typename T>
bool fgt(const T& x, const T& y) {
  return x > y + EPS;
}
template <typename T>
constexpr const T& _min(const T& x, const T& y) {
  return x < y ? x : y;
}
template <typename T>
constexpr const T& _max(const T& x, const T& y) {
  return x < y ? y : x;
}
template <typename T, typename... Ts>
constexpr const T& _min(const T& x, const Ts&... xs) {
  return _min(x, _min(xs...));
}
template <typename T, typename... Ts>
constexpr const T& _max(const T& x, const Ts&... xs) {
  return _max(x, _max(xs...));
}
template <typename T, typename... Ts>
void MIN(T& x, const Ts&... xs) {
  x = _min(x, xs...);
}
template <typename T, typename... Ts>
void MAX(T& x, const Ts&... xs) {
  x = _max(x, xs...);
}
template <typename T>
constexpr const T& _clamp(const T& v, const T& lo, const T& hi) {
  return v < lo ? lo : hi < v ? hi : v;
}
template <typename T>
void CLAMP(T& v, const T& lo, const T& hi) {
  v = _clamp(v, lo, hi);
}
template <typename T, typename... Args>
unique_ptr<T> _make_unique(Args&&... args) {
  return unique_ptr<T>(new T(forward<Args>(args)...));
}
template <typename T, typename... Args>
shared_ptr<T> _make_shared(Args&&... args) {
  return shared_ptr<T>(new T(forward<Args>(args)...));
}
template <typename... Ts>
using uset = unordered_set<Ts...>;
template <typename... Ts>
using umap = unordered_map<Ts...>;
template <typename... Ts>
using pq = priority_queue<Ts...>;
template <typename T>
using minpq = pq<T, vector<T>, greater<T>>;
template <typename T>
using maxpq = pq<T, vector<T>, less<T>>;
template <typename T1, typename T2, typename H1 = hash<T1>,
          typename H2 = hash<T2>>
struct pair_hash {
  size_t operator()(const pair<T1, T2>& p) const {
    return 31 * H1{}(p.first) + H2{}(p.second);
  }
};
seed_seq seq{(uint64_t)chrono::duration_cast<chrono::nanoseconds>(
                 chrono::high_resolution_clock::now().time_since_epoch())
                 .count(),
             (uint64_t)__builtin_ia32_rdtsc(),
             (uint64_t)(uintptr_t)_make_unique<char>().get()};
mt19937 rng(seq);
mt19937_64 rng64(seq);
constexpr int _bufferSize = 4096, _maxNumLength = 128;
char _inputBuffer[_bufferSize + 1],
    *_inputPtr = _inputBuffer, _outputBuffer[_bufferSize], _c, _sign,
    *_tempInputBuf = nullptr, _numBuf[_maxNumLength],
    _tempOutputBuf[_maxNumLength], _fill = ' ';
FILE *_input = stdin, *_output = stdout, *_error = stderr;
const char* _delimiter = " ";
int _cur, _outputPtr = 0, _numPtr = 0, _precision = 6, _width = 0,
          _tempOutputPtr = 0, _cnt;
ull _precisionBase = 1000000;
void read(int& x) {
  do {
    do {
      (x) = (*_inputPtr ? *_inputPtr++
                        : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                                              _bufferSize, _input)] = '\0',
                           *_inputPtr++));
    } while ((x) <= ' ');
    _sign = (x) == '-';
    if (_sign)
      (x) = (*_inputPtr ? *_inputPtr++
                        : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                                              _bufferSize, _input)] = '\0',
                           *_inputPtr++));
    for ((x) -= '0';
         (_c = (*_inputPtr ? *_inputPtr++
                           : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                             _bufferSize, _input)] = '\0',
                                          *_inputPtr++))) >= '0';
         (x) = (x)*10 + _c - '0')
      ;
    if (_sign) (x) = -(x);
  } while (0);
}
void read(uint& x) {
  do {
    do {
      (x) = (*_inputPtr ? *_inputPtr++
                        : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                                              _bufferSize, _input)] = '\0',
                           *_inputPtr++));
    } while ((x) <= ' ');
    _sign = (x) == '-';
    if (_sign)
      (x) = (*_inputPtr ? *_inputPtr++
                        : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                                              _bufferSize, _input)] = '\0',
                           *_inputPtr++));
    for ((x) -= '0';
         (_c = (*_inputPtr ? *_inputPtr++
                           : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                             _bufferSize, _input)] = '\0',
                                          *_inputPtr++))) >= '0';
         (x) = (x)*10 + _c - '0')
      ;
    if (_sign) (x) = -(x);
  } while (0);
}
void read(ll& x) {
  do {
    do {
      (x) = (*_inputPtr ? *_inputPtr++
                        : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                                              _bufferSize, _input)] = '\0',
                           *_inputPtr++));
    } while ((x) <= ' ');
    _sign = (x) == '-';
    if (_sign)
      (x) = (*_inputPtr ? *_inputPtr++
                        : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                                              _bufferSize, _input)] = '\0',
                           *_inputPtr++));
    for ((x) -= '0';
         (_c = (*_inputPtr ? *_inputPtr++
                           : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                             _bufferSize, _input)] = '\0',
                                          *_inputPtr++))) >= '0';
         (x) = (x)*10 + _c - '0')
      ;
    if (_sign) (x) = -(x);
  } while (0);
}
void read(ull& x) {
  do {
    do {
      (x) = (*_inputPtr ? *_inputPtr++
                        : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                                              _bufferSize, _input)] = '\0',
                           *_inputPtr++));
    } while ((x) <= ' ');
    _sign = (x) == '-';
    if (_sign)
      (x) = (*_inputPtr ? *_inputPtr++
                        : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                                              _bufferSize, _input)] = '\0',
                           *_inputPtr++));
    for ((x) -= '0';
         (_c = (*_inputPtr ? *_inputPtr++
                           : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                             _bufferSize, _input)] = '\0',
                                          *_inputPtr++))) >= '0';
         (x) = (x)*10 + _c - '0')
      ;
    if (_sign) (x) = -(x);
  } while (0);
}
void read(double& x) {
  do {
    do {
      (x) = (*_inputPtr ? *_inputPtr++
                        : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                                              _bufferSize, _input)] = '\0',
                           *_inputPtr++));
    } while ((x) <= ' ');
    _sign = (x) == '-';
    if (_sign)
      (x) = (*_inputPtr ? *_inputPtr++
                        : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                                              _bufferSize, _input)] = '\0',
                           *_inputPtr++));
    for ((x) -= '0';
         (_c = (*_inputPtr ? *_inputPtr++
                           : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                             _bufferSize, _input)] = '\0',
                                          *_inputPtr++))) >= '0';
         (x) = (x)*10 + _c - '0')
      ;
    if (_c == '.')
      for (double _div = 1.0;
           (_c = (*_inputPtr ? *_inputPtr++
                             : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                               _bufferSize, _input)] = '\0',
                                            *_inputPtr++))) >= '0';
           (x) += (_c - '0') / (_div *= 10))
        ;
    if (_sign) (x) = -(x);
  } while (0);
}
void read(ld& x) {
  do {
    do {
      (x) = (*_inputPtr ? *_inputPtr++
                        : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                                              _bufferSize, _input)] = '\0',
                           *_inputPtr++));
    } while ((x) <= ' ');
    _sign = (x) == '-';
    if (_sign)
      (x) = (*_inputPtr ? *_inputPtr++
                        : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                                              _bufferSize, _input)] = '\0',
                           *_inputPtr++));
    for ((x) -= '0';
         (_c = (*_inputPtr ? *_inputPtr++
                           : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                             _bufferSize, _input)] = '\0',
                                          *_inputPtr++))) >= '0';
         (x) = (x)*10 + _c - '0')
      ;
    if (_c == '.')
      for (ld _div = 1.0;
           (_c = (*_inputPtr ? *_inputPtr++
                             : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                               _bufferSize, _input)] = '\0',
                                            *_inputPtr++))) >= '0';
           (x) += (_c - '0') / (_div *= 10))
        ;
    if (_sign) (x) = -(x);
  } while (0);
}
void read(char& x) {
  do {
    do {
      (x) = (*_inputPtr ? *_inputPtr++
                        : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                                              _bufferSize, _input)] = '\0',
                           *_inputPtr++));
    } while ((x) <= ' ');
  } while (0);
}
void read(char* x) {
  do {
    _cur = 0;
    do {
      _c = (*_inputPtr ? *_inputPtr++
                       : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                                             _bufferSize, _input)] = '\0',
                          *_inputPtr++));
    } while (_c <= ' ');
    do {
      (x)[_cur++] = _c;
    } while (
        (_c = (*_inputPtr ? *_inputPtr++
                          : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                                                _bufferSize, _input)] = '\0',
                             *_inputPtr++))) > ' ');
    (x)[_cur] = '\0';
  } while (0);
}
void read(string& x) {
  do {
    if (!_tempInputBuf) assert(0);
    do {
      _cur = 0;
      do {
        _c = (*_inputPtr ? *_inputPtr++
                         : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                                               _bufferSize, _input)] = '\0',
                            *_inputPtr++));
      } while (_c <= ' ');
      do {
        (_tempInputBuf)[_cur++] = _c;
      } while (
          (_c = (*_inputPtr ? *_inputPtr++
                            : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                                                  _bufferSize, _input)] = '\0',
                               *_inputPtr++))) > ' ');
      (_tempInputBuf)[_cur] = '\0';
    } while (0);
    (x) = string(_tempInputBuf, _cur);
  } while (0);
}
template <typename T1, typename T2>
void read(pair<T1, T2>& x) {
  read(x.first);
  read(x.second);
}
template <typename T>
void read(complex<T>& x) {
  T _re, _im;
  read(_re);
  read(_im);
  x.real(_re);
  x.imag(_im);
}
bool hasNext() {
  while ((*_inputPtr || !feof(_input)) &&
         (*_inputPtr ? *_inputPtr
                     : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1,
                                           _bufferSize, _input)] = '\0',
                        *_inputPtr)) <= ' ')
    (*_inputPtr ? *_inputPtr++
                : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1, _bufferSize,
                                      _input)] = '\0',
                   *_inputPtr++));
  return (*_inputPtr || !feof(_input));
}
template <typename T, typename... Ts>
void read(T& x, Ts&... xs) {
  read(x);
  read(xs...);
}
void setInput(FILE* file) {
  *_inputPtr = '\0';
  _input = file;
}
void setInput(const char* second) {
  *_inputPtr = '\0';
  _input = fopen(second, "r");
}
void setInput(const string& second) {
  *_inputPtr = '\0';
  _input = fopen(second.c_str(), "r");
}
void writeDelimiter() {
  for (const char* _p = _delimiter; *_p;
       (_outputBuffer[_outputPtr == _bufferSize
                          ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                             _outputPtr = 0)
                          : _outputPtr] = (*_p++),
                            _outputPtr++))
    ;
}
void write(const bool& x) {
  do {
    if (x)
      (_tempOutputBuf[_tempOutputPtr++] = ('1'));
    else
      (_tempOutputBuf[_tempOutputPtr++] = ('0'));
    int _tempLen = _tempOutputPtr;
    for (int _i = 0; _i < (_width - _tempLen); _i++)
      (_outputBuffer[_outputPtr == _bufferSize
                         ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                            _outputPtr = 0)
                         : _outputPtr] = (_fill),
       _outputPtr++);
    for (int _i = 0; _i < _tempOutputPtr;
         (_outputBuffer[_outputPtr == _bufferSize
                            ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                               _outputPtr = 0)
                            : _outputPtr] = (_tempOutputBuf[_i++]),
                              _outputPtr++))
      ;
    _tempOutputPtr = 0;
    for (int _i = 0; _i < (-_width - _tempLen); _i++)
      (_outputBuffer[_outputPtr == _bufferSize
                         ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                            _outputPtr = 0)
                         : _outputPtr] = (_fill),
       _outputPtr++);
  } while (0);
}
void write(const int& x) {
  do {
    if ((x) < 0) {
      (_tempOutputBuf[_tempOutputPtr++] = ('-'));
      _cnt = 0;
      for (uint _y = (-(x)); _y; _y /= 10, _cnt++)
        _numBuf[_numPtr++] = '0' + _y % 10;
      for (; _cnt < 1; _cnt++) _numBuf[_numPtr++] = '0';
      for (; _numPtr; (_tempOutputBuf[_tempOutputPtr++] = (_numBuf[--_numPtr])))
        ;
      ;
    } else {
      _cnt = 0;
      for (uint _y = (x); _y; _y /= 10, _cnt++)
        _numBuf[_numPtr++] = '0' + _y % 10;
      for (; _cnt < 1; _cnt++) _numBuf[_numPtr++] = '0';
      for (; _numPtr; (_tempOutputBuf[_tempOutputPtr++] = (_numBuf[--_numPtr])))
        ;
      ;
    }
    int _tempLen = _tempOutputPtr;
    for (int _i = 0; _i < (_width - _tempLen); _i++)
      (_outputBuffer[_outputPtr == _bufferSize
                         ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                            _outputPtr = 0)
                         : _outputPtr] = (_fill),
       _outputPtr++);
    for (int _i = 0; _i < _tempOutputPtr;
         (_outputBuffer[_outputPtr == _bufferSize
                            ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                               _outputPtr = 0)
                            : _outputPtr] = (_tempOutputBuf[_i++]),
                              _outputPtr++))
      ;
    _tempOutputPtr = 0;
    for (int _i = 0; _i < (-_width - _tempLen); _i++)
      (_outputBuffer[_outputPtr == _bufferSize
                         ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                            _outputPtr = 0)
                         : _outputPtr] = (_fill),
       _outputPtr++);
  } while (0);
}
void write(const uint& x) {
  do {
    if ((x) < 0) {
      (_tempOutputBuf[_tempOutputPtr++] = ('-'));
      _cnt = 0;
      for (uint _y = (-(x)); _y; _y /= 10, _cnt++)
        _numBuf[_numPtr++] = '0' + _y % 10;
      for (; _cnt < 1; _cnt++) _numBuf[_numPtr++] = '0';
      for (; _numPtr; (_tempOutputBuf[_tempOutputPtr++] = (_numBuf[--_numPtr])))
        ;
      ;
    } else {
      _cnt = 0;
      for (uint _y = (x); _y; _y /= 10, _cnt++)
        _numBuf[_numPtr++] = '0' + _y % 10;
      for (; _cnt < 1; _cnt++) _numBuf[_numPtr++] = '0';
      for (; _numPtr; (_tempOutputBuf[_tempOutputPtr++] = (_numBuf[--_numPtr])))
        ;
      ;
    }
    int _tempLen = _tempOutputPtr;
    for (int _i = 0; _i < (_width - _tempLen); _i++)
      (_outputBuffer[_outputPtr == _bufferSize
                         ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                            _outputPtr = 0)
                         : _outputPtr] = (_fill),
       _outputPtr++);
    for (int _i = 0; _i < _tempOutputPtr;
         (_outputBuffer[_outputPtr == _bufferSize
                            ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                               _outputPtr = 0)
                            : _outputPtr] = (_tempOutputBuf[_i++]),
                              _outputPtr++))
      ;
    _tempOutputPtr = 0;
    for (int _i = 0; _i < (-_width - _tempLen); _i++)
      (_outputBuffer[_outputPtr == _bufferSize
                         ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                            _outputPtr = 0)
                         : _outputPtr] = (_fill),
       _outputPtr++);
  } while (0);
}
void write(const ll& x) {
  do {
    if ((x) < 0) {
      (_tempOutputBuf[_tempOutputPtr++] = ('-'));
      _cnt = 0;
      for (ull _y = (-(x)); _y; _y /= 10, _cnt++)
        _numBuf[_numPtr++] = '0' + _y % 10;
      for (; _cnt < 1; _cnt++) _numBuf[_numPtr++] = '0';
      for (; _numPtr; (_tempOutputBuf[_tempOutputPtr++] = (_numBuf[--_numPtr])))
        ;
      ;
    } else {
      _cnt = 0;
      for (ull _y = (x); _y; _y /= 10, _cnt++)
        _numBuf[_numPtr++] = '0' + _y % 10;
      for (; _cnt < 1; _cnt++) _numBuf[_numPtr++] = '0';
      for (; _numPtr; (_tempOutputBuf[_tempOutputPtr++] = (_numBuf[--_numPtr])))
        ;
      ;
    }
    int _tempLen = _tempOutputPtr;
    for (int _i = 0; _i < (_width - _tempLen); _i++)
      (_outputBuffer[_outputPtr == _bufferSize
                         ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                            _outputPtr = 0)
                         : _outputPtr] = (_fill),
       _outputPtr++);
    for (int _i = 0; _i < _tempOutputPtr;
         (_outputBuffer[_outputPtr == _bufferSize
                            ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                               _outputPtr = 0)
                            : _outputPtr] = (_tempOutputBuf[_i++]),
                              _outputPtr++))
      ;
    _tempOutputPtr = 0;
    for (int _i = 0; _i < (-_width - _tempLen); _i++)
      (_outputBuffer[_outputPtr == _bufferSize
                         ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                            _outputPtr = 0)
                         : _outputPtr] = (_fill),
       _outputPtr++);
  } while (0);
}
void write(const ull& x) {
  do {
    if ((x) < 0) {
      (_tempOutputBuf[_tempOutputPtr++] = ('-'));
      _cnt = 0;
      for (ull _y = (-(x)); _y; _y /= 10, _cnt++)
        _numBuf[_numPtr++] = '0' + _y % 10;
      for (; _cnt < 1; _cnt++) _numBuf[_numPtr++] = '0';
      for (; _numPtr; (_tempOutputBuf[_tempOutputPtr++] = (_numBuf[--_numPtr])))
        ;
      ;
    } else {
      _cnt = 0;
      for (ull _y = (x); _y; _y /= 10, _cnt++)
        _numBuf[_numPtr++] = '0' + _y % 10;
      for (; _cnt < 1; _cnt++) _numBuf[_numPtr++] = '0';
      for (; _numPtr; (_tempOutputBuf[_tempOutputPtr++] = (_numBuf[--_numPtr])))
        ;
      ;
    }
    int _tempLen = _tempOutputPtr;
    for (int _i = 0; _i < (_width - _tempLen); _i++)
      (_outputBuffer[_outputPtr == _bufferSize
                         ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                            _outputPtr = 0)
                         : _outputPtr] = (_fill),
       _outputPtr++);
    for (int _i = 0; _i < _tempOutputPtr;
         (_outputBuffer[_outputPtr == _bufferSize
                            ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                               _outputPtr = 0)
                            : _outputPtr] = (_tempOutputBuf[_i++]),
                              _outputPtr++))
      ;
    _tempOutputPtr = 0;
    for (int _i = 0; _i < (-_width - _tempLen); _i++)
      (_outputBuffer[_outputPtr == _bufferSize
                         ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                            _outputPtr = 0)
                         : _outputPtr] = (_fill),
       _outputPtr++);
  } while (0);
}
void write(const double& x) {
  do {
    if (std::isnan(x)) {
      do {
        int _slen = strlen("NaN");
        for (int _i = 0; _i < (_width - _slen); _i++)
          (_outputBuffer[_outputPtr == _bufferSize
                             ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                                _outputPtr = 0)
                             : _outputPtr] = (_fill),
           _outputPtr++);
        for (const char* _p = ("NaN"); *_p;
             (_outputBuffer[_outputPtr == _bufferSize
                                ? (fwrite(_outputBuffer, 1, _outputPtr,
                                          _output),
                                   _outputPtr = 0)
                                : _outputPtr] = (*_p++),
                                  _outputPtr++))
          ;
        for (int _i = 0; _i < (-_width - _slen); _i++)
          (_outputBuffer[_outputPtr == _bufferSize
                             ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                                _outputPtr = 0)
                             : _outputPtr] = (_fill),
           _outputPtr++);
      } while (0);
    } else if (std::isinf(x)) {
      do {
        int _slen = strlen("Inf");
        for (int _i = 0; _i < (_width - _slen); _i++)
          (_outputBuffer[_outputPtr == _bufferSize
                             ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                                _outputPtr = 0)
                             : _outputPtr] = (_fill),
           _outputPtr++);
        for (const char* _p = ("Inf"); *_p;
             (_outputBuffer[_outputPtr == _bufferSize
                                ? (fwrite(_outputBuffer, 1, _outputPtr,
                                          _output),
                                   _outputPtr = 0)
                                : _outputPtr] = (*_p++),
                                  _outputPtr++))
          ;
        for (int _i = 0; _i < (-_width - _slen); _i++)
          (_outputBuffer[_outputPtr == _bufferSize
                             ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                                _outputPtr = 0)
                             : _outputPtr] = (_fill),
           _outputPtr++);
      } while (0);
    } else if ((x) < 0) {
      (_tempOutputBuf[_tempOutputPtr++] = ('-'));
      ull _I = (ull)(-(x));
      ull _F = ((-(x)) - _I) * _precisionBase + (double)(0.5);
      if (_F >= _precisionBase) {
        _I++;
        _F = 0;
      }
      _cnt = 0;
      for (ull _y = (_I); _y; _y /= 10, _cnt++)
        _numBuf[_numPtr++] = '0' + _y % 10;
      for (; _cnt < 1; _cnt++) _numBuf[_numPtr++] = '0';
      for (; _numPtr; (_tempOutputBuf[_tempOutputPtr++] = (_numBuf[--_numPtr])))
        ;
      ;
      (_tempOutputBuf[_tempOutputPtr++] = ('.'));
      _cnt = 0;
      for (ull _y = (_F); _y; _y /= 10, _cnt++)
        _numBuf[_numPtr++] = '0' + _y % 10;
      for (; _cnt < _precision; _cnt++) _numBuf[_numPtr++] = '0';
      for (; _numPtr; (_tempOutputBuf[_tempOutputPtr++] = (_numBuf[--_numPtr])))
        ;
      ;
    } else {
      ull _I = (ull)(x);
      ull _F = ((x)-_I) * _precisionBase + (double)(0.5);
      if (_F >= _precisionBase) {
        _I++;
        _F = 0;
      }
      _cnt = 0;
      for (ull _y = (_I); _y; _y /= 10, _cnt++)
        _numBuf[_numPtr++] = '0' + _y % 10;
      for (; _cnt < 1; _cnt++) _numBuf[_numPtr++] = '0';
      for (; _numPtr; (_tempOutputBuf[_tempOutputPtr++] = (_numBuf[--_numPtr])))
        ;
      ;
      (_tempOutputBuf[_tempOutputPtr++] = ('.'));
      _cnt = 0;
      for (ull _y = (_F); _y; _y /= 10, _cnt++)
        _numBuf[_numPtr++] = '0' + _y % 10;
      for (; _cnt < _precision; _cnt++) _numBuf[_numPtr++] = '0';
      for (; _numPtr; (_tempOutputBuf[_tempOutputPtr++] = (_numBuf[--_numPtr])))
        ;
      ;
    }
    int _tempLen = _tempOutputPtr;
    for (int _i = 0; _i < (_width - _tempLen); _i++)
      (_outputBuffer[_outputPtr == _bufferSize
                         ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                            _outputPtr = 0)
                         : _outputPtr] = (_fill),
       _outputPtr++);
    for (int _i = 0; _i < _tempOutputPtr;
         (_outputBuffer[_outputPtr == _bufferSize
                            ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                               _outputPtr = 0)
                            : _outputPtr] = (_tempOutputBuf[_i++]),
                              _outputPtr++))
      ;
    _tempOutputPtr = 0;
    for (int _i = 0; _i < (-_width - _tempLen); _i++)
      (_outputBuffer[_outputPtr == _bufferSize
                         ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                            _outputPtr = 0)
                         : _outputPtr] = (_fill),
       _outputPtr++);
  } while (0);
}
void write(const ld& x) {
  do {
    if (std::isnan(x)) {
      do {
        int _slen = strlen("NaN");
        for (int _i = 0; _i < (_width - _slen); _i++)
          (_outputBuffer[_outputPtr == _bufferSize
                             ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                                _outputPtr = 0)
                             : _outputPtr] = (_fill),
           _outputPtr++);
        for (const char* _p = ("NaN"); *_p;
             (_outputBuffer[_outputPtr == _bufferSize
                                ? (fwrite(_outputBuffer, 1, _outputPtr,
                                          _output),
                                   _outputPtr = 0)
                                : _outputPtr] = (*_p++),
                                  _outputPtr++))
          ;
        for (int _i = 0; _i < (-_width - _slen); _i++)
          (_outputBuffer[_outputPtr == _bufferSize
                             ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                                _outputPtr = 0)
                             : _outputPtr] = (_fill),
           _outputPtr++);
      } while (0);
    } else if (std::isinf(x)) {
      do {
        int _slen = strlen("Inf");
        for (int _i = 0; _i < (_width - _slen); _i++)
          (_outputBuffer[_outputPtr == _bufferSize
                             ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                                _outputPtr = 0)
                             : _outputPtr] = (_fill),
           _outputPtr++);
        for (const char* _p = ("Inf"); *_p;
             (_outputBuffer[_outputPtr == _bufferSize
                                ? (fwrite(_outputBuffer, 1, _outputPtr,
                                          _output),
                                   _outputPtr = 0)
                                : _outputPtr] = (*_p++),
                                  _outputPtr++))
          ;
        for (int _i = 0; _i < (-_width - _slen); _i++)
          (_outputBuffer[_outputPtr == _bufferSize
                             ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                                _outputPtr = 0)
                             : _outputPtr] = (_fill),
           _outputPtr++);
      } while (0);
    } else if ((x) < 0) {
      (_tempOutputBuf[_tempOutputPtr++] = ('-'));
      ull _I = (ull)(-(x));
      ull _F = ((-(x)) - _I) * _precisionBase + (ld)(0.5);
      if (_F >= _precisionBase) {
        _I++;
        _F = 0;
      }
      _cnt = 0;
      for (ull _y = (_I); _y; _y /= 10, _cnt++)
        _numBuf[_numPtr++] = '0' + _y % 10;
      for (; _cnt < 1; _cnt++) _numBuf[_numPtr++] = '0';
      for (; _numPtr; (_tempOutputBuf[_tempOutputPtr++] = (_numBuf[--_numPtr])))
        ;
      ;
      (_tempOutputBuf[_tempOutputPtr++] = ('.'));
      _cnt = 0;
      for (ull _y = (_F); _y; _y /= 10, _cnt++)
        _numBuf[_numPtr++] = '0' + _y % 10;
      for (; _cnt < _precision; _cnt++) _numBuf[_numPtr++] = '0';
      for (; _numPtr; (_tempOutputBuf[_tempOutputPtr++] = (_numBuf[--_numPtr])))
        ;
      ;
    } else {
      ull _I = (ull)(x);
      ull _F = ((x)-_I) * _precisionBase + (ld)(0.5);
      if (_F >= _precisionBase) {
        _I++;
        _F = 0;
      }
      _cnt = 0;
      for (ull _y = (_I); _y; _y /= 10, _cnt++)
        _numBuf[_numPtr++] = '0' + _y % 10;
      for (; _cnt < 1; _cnt++) _numBuf[_numPtr++] = '0';
      for (; _numPtr; (_tempOutputBuf[_tempOutputPtr++] = (_numBuf[--_numPtr])))
        ;
      ;
      (_tempOutputBuf[_tempOutputPtr++] = ('.'));
      _cnt = 0;
      for (ull _y = (_F); _y; _y /= 10, _cnt++)
        _numBuf[_numPtr++] = '0' + _y % 10;
      for (; _cnt < _precision; _cnt++) _numBuf[_numPtr++] = '0';
      for (; _numPtr; (_tempOutputBuf[_tempOutputPtr++] = (_numBuf[--_numPtr])))
        ;
      ;
    }
    int _tempLen = _tempOutputPtr;
    for (int _i = 0; _i < (_width - _tempLen); _i++)
      (_outputBuffer[_outputPtr == _bufferSize
                         ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                            _outputPtr = 0)
                         : _outputPtr] = (_fill),
       _outputPtr++);
    for (int _i = 0; _i < _tempOutputPtr;
         (_outputBuffer[_outputPtr == _bufferSize
                            ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                               _outputPtr = 0)
                            : _outputPtr] = (_tempOutputBuf[_i++]),
                              _outputPtr++))
      ;
    _tempOutputPtr = 0;
    for (int _i = 0; _i < (-_width - _tempLen); _i++)
      (_outputBuffer[_outputPtr == _bufferSize
                         ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                            _outputPtr = 0)
                         : _outputPtr] = (_fill),
       _outputPtr++);
  } while (0);
}
void write(const char& x) {
  do {
    (_tempOutputBuf[_tempOutputPtr++] = (x));
    int _tempLen = _tempOutputPtr;
    for (int _i = 0; _i < (_width - _tempLen); _i++)
      (_outputBuffer[_outputPtr == _bufferSize
                         ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                            _outputPtr = 0)
                         : _outputPtr] = (_fill),
       _outputPtr++);
    for (int _i = 0; _i < _tempOutputPtr;
         (_outputBuffer[_outputPtr == _bufferSize
                            ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                               _outputPtr = 0)
                            : _outputPtr] = (_tempOutputBuf[_i++]),
                              _outputPtr++))
      ;
    _tempOutputPtr = 0;
    for (int _i = 0; _i < (-_width - _tempLen); _i++)
      (_outputBuffer[_outputPtr == _bufferSize
                         ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                            _outputPtr = 0)
                         : _outputPtr] = (_fill),
       _outputPtr++);
  } while (0);
}
void write(const char* x) {
  do {
    int _slen = strlen(x);
    for (int _i = 0; _i < (_width - _slen); _i++)
      (_outputBuffer[_outputPtr == _bufferSize
                         ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                            _outputPtr = 0)
                         : _outputPtr] = (_fill),
       _outputPtr++);
    for (const char* _p = (x); *_p;
         (_outputBuffer[_outputPtr == _bufferSize
                            ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                               _outputPtr = 0)
                            : _outputPtr] = (*_p++),
                              _outputPtr++))
      ;
    for (int _i = 0; _i < (-_width - _slen); _i++)
      (_outputBuffer[_outputPtr == _bufferSize
                         ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                            _outputPtr = 0)
                         : _outputPtr] = (_fill),
       _outputPtr++);
  } while (0);
}
void write(const string& x) {
  do {
    for (int _i = 0; _i < (_width - (int)(x).length()); _i++)
      (_outputBuffer[_outputPtr == _bufferSize
                         ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                            _outputPtr = 0)
                         : _outputPtr] = (_fill),
       _outputPtr++);
    for (int _i = 0; _i < (int)(x).length();
         (_outputBuffer[_outputPtr == _bufferSize
                            ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                               _outputPtr = 0)
                            : _outputPtr] = (x[_i++]),
                              _outputPtr++))
      ;
    for (int _i = 0; _i < (-_width - (int)(x).length()); _i++)
      (_outputBuffer[_outputPtr == _bufferSize
                         ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                            _outputPtr = 0)
                         : _outputPtr] = (_fill),
       _outputPtr++);
  } while (0);
}
template <typename T1, typename T2>
void write(const pair<T1, T2>& x) {
  write(x.first);
  writeDelimiter();
  write(x.second);
}
template <typename T>
void write(const complex<T>& x) {
  write(x.real());
  writeDelimiter();
  write(x.imag());
}
template <typename T>
void write(const T& x) {
  bool _first = 1;
  for (auto&& _i : x) {
    if (_first)
      _first = 0;
    else
      writeDelimiter();
    write(_i);
  }
}
template <typename T, typename... Ts>
void write(const T& x, const Ts&... xs) {
  write(x);
  writeDelimiter();
  write(xs...);
}
void writeln() {
  (_outputBuffer[_outputPtr == _bufferSize
                     ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                        _outputPtr = 0)
                     : _outputPtr] = ('\n'),
   _outputPtr++);
}
template <typename... Ts>
void writeln(const Ts&... xs) {
  write(xs...);
  (_outputBuffer[_outputPtr == _bufferSize
                     ? (fwrite(_outputBuffer, 1, _outputPtr, _output),
                        _outputPtr = 0)
                     : _outputPtr] = ('\n'),
   _outputPtr++);
}
void flush() {
  do {
    (fwrite(_outputBuffer, 1, _outputPtr, _output), _outputPtr = 0);
    fflush(_output);
  } while (0);
}
class IOManager {
 public:
  ~IOManager() { flush(); }
};
unique_ptr<IOManager> iomanager = _make_unique<IOManager>();
int N;
ll A[150000], B[150000];
int main() {
  do {
    _delimiter = ("");
  } while (0);
  read(N);
  for (auto i = (0); i < (N); i++) {
    read(B[i]);
    A[i] = B[i];
  }
  for (auto i = (1); i < (N); i++) {
    if (B[i] != B[0]) break;
    if (i == N - 1) {
      if (B[0] != 0)
        writeln("NO");
      else {
        writeln("YES");
        for (auto j = (0); j < (N); j++) write(1, " \n"[j == N - 1]);
      }
      return 0;
    }
  }
  writeln("YES");
  for (auto i = (0); i < (N); i++) {
    if (B[i] < B[(i + 1) % N]) {
      int j = i;
      while (A[j] == 0 || A[(j + N - 1) % N] % A[j] != B[(j + N - 1) % N]) {
        A[j] +=
            ((A[(j + N - 1) % N] - A[j]) / A[(j + 1) % N] + 1) * A[(j + 1) % N];
        j = (j + N - 1) % N;
      }
    }
  }
  for (auto i = (0); i < (N); i++) write(A[i], " \n"[i == N - 1]);
  return 0;
}
