#include <bits/stdc++.h>
using namespace std;
template <class T>
void splitstr(const string &s, vector<T> &out) {
  istringstream in(s);
  out.clear();
  copy(istream_iterator<T>(in), istream_iterator<T>(), back_inserter(out));
}
template <class T>
T read_value(string s) {
  T result;
  istringstream sin(s);
  sin >> result;
  return result;
}
string read_line() {
  string ret_val;
  getline(std::cin, ret_val);
  return ret_val;
}
template <class T>
void init_array(T *arr, int size, T value) {
  for (int i = 0; i < size; i++) arr[i] = value;
}
template <class T>
inline T gcd(T a, T b) {
  return (!a) ? b : gcd(b % a, a);
}
template <class T>
inline T mod(T a, T p) {
  a %= p;
  return (a < 0) ? a + p : a;
}
template <class T>
inline int numbits(T n) {
  return (!n) ? 0 : 1 + numbits(n & (n - 1));
}
template <class T>
inline T inverse(T a, T m) {
  a = mod<T>(a, m);
  return (a == 1) ? 1 : mod((1 - m * inverse(m % a, a)) / a, m);
}
template <class T>
inline bool is_prime(T a) {
  T lim = (T)sqrt((double)a);
  for (T i = 2; i <= T(lim + 1E-9); i++)
    if (a % i == 0) return false;
  return true;
}
template <class T>
inline T power(T a, T p, T mod) {
  if (!p) return 1;
  T temp = power(a, p >> 1, mod);
  temp = (temp * temp) % mod;
  if (p & 1) temp = (temp * a) % mod;
  return temp;
}
void get_primes(int start, int end, vector<int> &vi) {
  bool *p = new bool[end + 1];
  init_array<bool>(p, end + 1, 0);
  p[1] = 1;
  for (int i = 2; i <= end; i++) {
    if (!p[i]) {
      if (i >= start) vi.push_back(i);
      for (int j = 2 * i; j <= end; j += i) p[j] = 1;
    }
  }
  delete[] p;
}
bool dfs(int current, int final, int total, vector<int> &visited,
         vector<vector<bool> > &edges, bool flow) {
  if (current == final) return true;
  if (visited[current]) return false;
  visited[current] = true;
  for (int i = 0; i < total; i++)
    if (edges[current][i] && dfs(i, final, total, visited, edges, flow)) {
      if (flow) {
        edges[current][i] = false;
        edges[i][current] = true;
      }
      return true;
    }
  return false;
}
int flow(int in, int out, int total, vector<vector<bool> > &edges) {
  int result = 0;
  for (vector<int> visited(total, 0); dfs(in, out, total, visited, edges, true);
       ++result)
    visited = vector<int>(total, 0);
  return result;
}
void create_set(int x, int *P, int *rank) {
  P[x] = x;
  rank[x] = 0;
}
int find_set(int x, int *P) {
  if (x != P[x]) P[x] = find_set(P[x], P);
  return P[x];
}
bool merge_sets(int x, int y, int *P, int *rank) {
  int Px = find_set(x, P);
  int Py = find_set(y, P);
  if (Px == Py) return false;
  if (rank[Px] > rank[Py])
    P[Py] = Px;
  else
    P[Px] = Py;
  if (rank[Px] == rank[Py]) rank[Py]++;
  return true;
}
template <typename T>
int read_cum_freq(int index, T *tree) {
  int sum = 0;
  while (index) {
    sum += tree[index];
    index -= (index & -index);
  }
  return sum;
}
template <typename T>
void upd_freq(int index, int mxIndex, int value, T *tree) {
  while (index <= mxIndex) {
    tree[index] += value;
    index += (index & -index);
  }
}
template <typename T>
int read_freq(int index, T *tree) {
  return read_cum_freq(index, tree) - read_cum_freq(index - 1, tree);
}
void build_failure_function(const string &str, int *temp_arr) {
  temp_arr[0] = temp_arr[1] = 0;
  for (int i = 2; i <= ((int)(str).size()); i++) {
    temp_arr[i] = -1;
    for (int ind = temp_arr[i - 1]; temp_arr[i] == -1; ind = temp_arr[ind]) {
      if (str[ind] == str[i - 1]) {
        temp_arr[i] = ind + 1;
      } else if (ind == 0) {
        temp_arr[i] = 0;
      }
    }
  }
}
void KMP(const string &text, const string &pattern, int *res) {
  int *temp_arr = new int[((int)(pattern).size()) + 1];
  build_failure_function(pattern, temp_arr);
  int i = 0;
  int ind = 0;
  while (i < ((int)(text).size())) {
    if (text[i] == pattern[ind]) {
      res[i] = ++ind;
      if (res[i] == ((int)(pattern).size())) {
        ind = temp_arr[ind];
      }
      i++;
    } else if (ind == 0) {
      res[i++] = 0;
    } else {
      ind = temp_arr[ind];
    }
  }
  delete[] temp_arr;
}
template <typename T, int N>
struct matrix {
  T m[N][N];
  T md;
  matrix(T md, bool unary = false) {
    this->md = md;
    memset(m, 0, sizeof(m));
    if (unary) {
      for (int i = 0; i < N; i++) {
        m[i][i] = 1;
      }
    }
  }
  matrix operator*(const matrix &that) const {
    matrix ret_val(md, false);
    for (int i = 0; i < N; i++) {
      for (int j = 0; j < N; j++) {
        for (int k = 0; k < N; k++) {
          ret_val.m[i][j] += this->m[i][k] * that.m[k][j];
          ret_val.m[i][j] %= md;
        }
      }
    }
    return ret_val;
  }
  vector<T> operator*(const vector<T> &vec) const {
    vector<T> ret_val(vec.size(), 0);
    for (int i = 0; i < N; i++) {
      for (int j = 0; j < N; j++) {
        ret_val[i] += m[i][j] * vec[j];
        ret_val[i] %= md;
      }
    }
    return ret_val;
  }
  matrix power(int pw) const {
    if (!pw) return matrix(md, true);
    if (pw == 1) return *this;
    matrix ret_val = power(pw >> 1);
    ret_val = ret_val * ret_val;
    if (pw & 1) ret_val = ret_val * (*this);
    return ret_val;
  }
};
void setup(int value, string name) {
  string name_in = name + ".in";
  string name_out = name + ".out";
  freopen(name_in.c_str(), "r", stdin);
  if (value) freopen(name_out.c_str(), "w", stdout);
}
int main() {
  int n;
  std::cin >> n;
  std::vector<int> vi(n);
  for (int i = 0; i < n; ++i) {
    scanf("%d", &vi[i]);
  }
  sort(vi.begin(), vi.end());
  if (vi[0] == vi.back() && vi[0] == 1) {
    for (int i = 0; i < vi.size() - 1; ++i) {
      std::cout << "1 ";
    }
    std::cout << "2\n";
  } else {
    std::cout << "1 ";
    for (int i = 0; i < vi.size() - 1; ++i) {
      std::cout << vi[i] << " ";
    }
    std::cout << std::endl;
  }
  return 0;
}

### Prompt

Please provide a CPP coded solution to the problem described below:

Little Petya very much likes arrays consisting of n integers, where each of them is in the range from 1 to 109, inclusive. Recently he has received one such array as a gift from his mother. Petya didn't like it at once. He decided to choose exactly one element from the array and replace it with another integer that also lies in the range from 1 to 109, inclusive. It is not allowed to replace a number with itself or to change no number at all. 

After the replacement Petya sorted the array by the numbers' non-decreasing. Now he wants to know for each position: what minimum number could occupy it after the replacement and the sorting.

Input

The first line contains a single integer n (1 ≤ n ≤ 105), which represents how many numbers the array has. The next line contains n space-separated integers — the array's description. All elements of the array lie in the range from 1 to 109, inclusive.

Output

Print n space-separated integers — the minimum possible values of each array element after one replacement and the sorting are performed.

Examples

Input

5
1 2 3 4 5


Output

1 1 2 3 4


Input

5
2 3 4 5 6


Output

1 2 3 4 5


Input

3
2 2 2


Output

1 2 2

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <class T>
void splitstr(const string &s, vector<T> &out) {
  istringstream in(s);
  out.clear();
  copy(istream_iterator<T>(in), istream_iterator<T>(), back_inserter(out));
}
template <class T>
T read_value(string s) {
  T result;
  istringstream sin(s);
  sin >> result;
  return result;
}
string read_line() {
  string ret_val;
  getline(std::cin, ret_val);
  return ret_val;
}
template <class T>
void init_array(T *arr, int size, T value) {
  for (int i = 0; i < size; i++) arr[i] = value;
}
template <class T>
inline T gcd(T a, T b) {
  return (!a) ? b : gcd(b % a, a);
}
template <class T>
inline T mod(T a, T p) {
  a %= p;
  return (a < 0) ? a + p : a;
}
template <class T>
inline int numbits(T n) {
  return (!n) ? 0 : 1 + numbits(n & (n - 1));
}
template <class T>
inline T inverse(T a, T m) {
  a = mod<T>(a, m);
  return (a == 1) ? 1 : mod((1 - m * inverse(m % a, a)) / a, m);
}
template <class T>
inline bool is_prime(T a) {
  T lim = (T)sqrt((double)a);
  for (T i = 2; i <= T(lim + 1E-9); i++)
    if (a % i == 0) return false;
  return true;
}
template <class T>
inline T power(T a, T p, T mod) {
  if (!p) return 1;
  T temp = power(a, p >> 1, mod);
  temp = (temp * temp) % mod;
  if (p & 1) temp = (temp * a) % mod;
  return temp;
}
void get_primes(int start, int end, vector<int> &vi) {
  bool *p = new bool[end + 1];
  init_array<bool>(p, end + 1, 0);
  p[1] = 1;
  for (int i = 2; i <= end; i++) {
    if (!p[i]) {
      if (i >= start) vi.push_back(i);
      for (int j = 2 * i; j <= end; j += i) p[j] = 1;
    }
  }
  delete[] p;
}
bool dfs(int current, int final, int total, vector<int> &visited,
         vector<vector<bool> > &edges, bool flow) {
  if (current == final) return true;
  if (visited[current]) return false;
  visited[current] = true;
  for (int i = 0; i < total; i++)
    if (edges[current][i] && dfs(i, final, total, visited, edges, flow)) {
      if (flow) {
        edges[current][i] = false;
        edges[i][current] = true;
      }
      return true;
    }
  return false;
}
int flow(int in, int out, int total, vector<vector<bool> > &edges) {
  int result = 0;
  for (vector<int> visited(total, 0); dfs(in, out, total, visited, edges, true);
       ++result)
    visited = vector<int>(total, 0);
  return result;
}
void create_set(int x, int *P, int *rank) {
  P[x] = x;
  rank[x] = 0;
}
int find_set(int x, int *P) {
  if (x != P[x]) P[x] = find_set(P[x], P);
  return P[x];
}
bool merge_sets(int x, int y, int *P, int *rank) {
  int Px = find_set(x, P);
  int Py = find_set(y, P);
  if (Px == Py) return false;
  if (rank[Px] > rank[Py])
    P[Py] = Px;
  else
    P[Px] = Py;
  if (rank[Px] == rank[Py]) rank[Py]++;
  return true;
}
template <typename T>
int read_cum_freq(int index, T *tree) {
  int sum = 0;
  while (index) {
    sum += tree[index];
    index -= (index & -index);
  }
  return sum;
}
template <typename T>
void upd_freq(int index, int mxIndex, int value, T *tree) {
  while (index <= mxIndex) {
    tree[index] += value;
    index += (index & -index);
  }
}
template <typename T>
int read_freq(int index, T *tree) {
  return read_cum_freq(index, tree) - read_cum_freq(index - 1, tree);
}
void build_failure_function(const string &str, int *temp_arr) {
  temp_arr[0] = temp_arr[1] = 0;
  for (int i = 2; i <= ((int)(str).size()); i++) {
    temp_arr[i] = -1;
    for (int ind = temp_arr[i - 1]; temp_arr[i] == -1; ind = temp_arr[ind]) {
      if (str[ind] == str[i - 1]) {
        temp_arr[i] = ind + 1;
      } else if (ind == 0) {
        temp_arr[i] = 0;
      }
    }
  }
}
void KMP(const string &text, const string &pattern, int *res) {
  int *temp_arr = new int[((int)(pattern).size()) + 1];
  build_failure_function(pattern, temp_arr);
  int i = 0;
  int ind = 0;
  while (i < ((int)(text).size())) {
    if (text[i] == pattern[ind]) {
      res[i] = ++ind;
      if (res[i] == ((int)(pattern).size())) {
        ind = temp_arr[ind];
      }
      i++;
    } else if (ind == 0) {
      res[i++] = 0;
    } else {
      ind = temp_arr[ind];
    }
  }
  delete[] temp_arr;
}
template <typename T, int N>
struct matrix {
  T m[N][N];
  T md;
  matrix(T md, bool unary = false) {
    this->md = md;
    memset(m, 0, sizeof(m));
    if (unary) {
      for (int i = 0; i < N; i++) {
        m[i][i] = 1;
      }
    }
  }
  matrix operator*(const matrix &that) const {
    matrix ret_val(md, false);
    for (int i = 0; i < N; i++) {
      for (int j = 0; j < N; j++) {
        for (int k = 0; k < N; k++) {
          ret_val.m[i][j] += this->m[i][k] * that.m[k][j];
          ret_val.m[i][j] %= md;
        }
      }
    }
    return ret_val;
  }
  vector<T> operator*(const vector<T> &vec) const {
    vector<T> ret_val(vec.size(), 0);
    for (int i = 0; i < N; i++) {
      for (int j = 0; j < N; j++) {
        ret_val[i] += m[i][j] * vec[j];
        ret_val[i] %= md;
      }
    }
    return ret_val;
  }
  matrix power(int pw) const {
    if (!pw) return matrix(md, true);
    if (pw == 1) return *this;
    matrix ret_val = power(pw >> 1);
    ret_val = ret_val * ret_val;
    if (pw & 1) ret_val = ret_val * (*this);
    return ret_val;
  }
};
void setup(int value, string name) {
  string name_in = name + ".in";
  string name_out = name + ".out";
  freopen(name_in.c_str(), "r", stdin);
  if (value) freopen(name_out.c_str(), "w", stdout);
}
int main() {
  int n;
  std::cin >> n;
  std::vector<int> vi(n);
  for (int i = 0; i < n; ++i) {
    scanf("%d", &vi[i]);
  }
  sort(vi.begin(), vi.end());
  if (vi[0] == vi.back() && vi[0] == 1) {
    for (int i = 0; i < vi.size() - 1; ++i) {
      std::cout << "1 ";
    }
    std::cout << "2\n";
  } else {
    std::cout << "1 ";
    for (int i = 0; i < vi.size() - 1; ++i) {
      std::cout << vi[i] << " ";
    }
    std::cout << std::endl;
  }
  return 0;
}

```