#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline void read(T &x) {
  static char _c;
  static bool _f;
  x = 0;
  _f = 0;
  _c = getchar();
  while (_c < '0' || '9' < _c) {
    if (_c == '-') _f = true;
    _c = getchar();
  }
  while ('0' <= _c && _c <= '9') {
    x = (x << 1) + (x << 3) + (_c & 15);
    _c = getchar();
  }
  if (_f) x = -x;
}
template <typename T>
inline void Min(T &x, T y) {
  if (y < x) x = y;
}
template <typename T>
inline void Max(T &x, T y) {
  if (x < y) x = y;
}
const int INF = 0x3f3f3f3f;
const double pi = (double)acos(-1.0);
const double eps = (double)1e-8;
const int e5 = (int)1e5 + 5;
const int MOD = (int)1e9 + 7;
inline int sig(double x) { return x < -eps ? -1 : eps < x; }
long long fp(long long a, long long n, long long mod = MOD) {
  if (n < 0) a = fp(a, mod - 2, mod), n = -n;
  long long res = 1;
  for (; n; n >>= 1, a = a * a % mod)
    if (n & 1) res = res * a % mod;
  return res;
}
struct Mint {
  int x;
  Mint() { x = 0; }
  Mint(int _x) : x(_x) {
    if (x < 0 || x >= MOD) x = (x % MOD + MOD) % MOD;
  }
  Mint(long long _x) : x(_x) {
    if (x < 0 || x >= MOD) x = (x % MOD + MOD) % MOD;
  }
  Mint operator-() const { return Mint(MOD - x); }
  Mint operator+(const Mint &rhs) const {
    return Mint(x + rhs.x >= MOD ? x + rhs.x - MOD : x + rhs.x);
  }
  Mint operator-(const Mint &rhs) const {
    return Mint(x - rhs.x < 0 ? x - rhs.x + MOD : x - rhs.x);
  }
  Mint operator*(const Mint &rhs) const {
    return Mint((long long)x * rhs.x % MOD);
  }
  Mint operator/(const Mint &rhs) const {
    return Mint(x * fp(rhs.x, -1) % MOD);
  }
  Mint &operator+=(const Mint &rhs) {
    x += rhs.x;
    if (x >= MOD) x -= MOD;
    return *this;
  }
  Mint &operator*=(const Mint &rhs) {
    x = ((long long)x * rhs.x) % MOD;
    return *this;
  }
  bool operator==(const Mint &rhs) const { return x == rhs.x; }
  bool operator!=(const Mint &rhs) const { return x != rhs.x; }
  friend ostream &operator<<(ostream &out, const Mint &rhs) {
    return out << rhs.x;
  }
  friend istream &operator>>(istream &in, Mint &rhs) { return in >> rhs.x; }
};
const int maxn = (int)2e5 + 20;
const int maxm = (int)1e6 + 20;
const int N = 500 + 5;
struct PQ_tree {
  int n, tot;
  int fail;
  vector<int> G[N << 2];
  int ty[N << 2];
  int sz[N << 2];
  int szc[N << 2];
  bool s[N];
  inline int getstate(int u) {
    if (szc[u] == 0) return 0;
    if (szc[u] == sz[u]) return 2;
    return 1;
  }
  void addson(int x, int y) {
    if (y) G[x].push_back(y);
  }
  void join(int x, int y) {
    for (auto v : G[y]) G[x].push_back(v);
  }
  int mergeP(vector<int> &vec) {
    if (vec.size() == 0) return 0;
    if (vec.size() == 1) return vec[0];
    G[++tot] = vec;
    return tot;
  }
  void init(int _n) {
    n = _n;
    tot = n + 1;
    memset(ty, 0, sizeof(ty));
    for (int i = 1; i <= n; i++) G[n + 1].push_back(i);
    fail = 0;
  }
  void dfs(int u) {
    sz[u] = u <= n;
    szc[u] = u <= n && s[u];
    for (auto v : G[u]) {
      dfs(v);
      sz[u] += sz[v];
      szc[u] += szc[v];
    }
  }
  int check(int u, int t) {
    if (fail) return 0;
    vector<int> vec[3];
    for (auto v : G[u]) vec[getstate(v)].push_back(v);
    if (vec[1].size() > 2 || (t && vec[1].size() > 1)) return fail = 1, 0;
    if (t == 0 && vec[1].size() == 1 && vec[2].size() == 0)
      return check(vec[1][0], 0);
    if (ty[u] == 0) {
      int p2 = mergeP(vec[2]);
      if (t == 0) {
        G[u] = vec[0];
        if (vec[1].size() == 0)
          addson(u, p2);
        else {
          int tmp1 = check(vec[1][0], 2);
          addson(tmp1, p2);
          if (vec[1].size() == 2) join(tmp1, check(vec[1][1], 1));
          addson(u, tmp1);
        }
        return u;
      } else {
        ty[u] = 1;
        G[u].clear();
        addson(u, p2);
        if (vec[1].size() == 1) join(u, check(vec[1][0], 1));
        addson(u, mergeP(vec[0]));
        if (t == 2) reverse(G[u].begin(), G[u].end());
      }
      return u;
    } else {
      if (getstate(G[u].front()) > getstate(G[u].back()))
        reverse(G[u].begin(), G[u].end());
      int flag = 0;
      vector<int> tG;
      for (auto v : G[u]) {
        int sta = getstate(v);
        if (sta == 0) {
          if (flag == 1) flag = 2;
          tG.push_back(v);
        } else if (sta == 2) {
          if (flag == 0)
            flag = 1;
          else if (flag == 2)
            return fail = 2, 0;
          tG.push_back(v);
        } else {
          int p1;
          if (flag == 0)
            flag = 1, p1 = check(v, 2);
          else if (flag == 1)
            flag = 2, p1 = check(v, 1);
          else
            return fail = 3, 0;
          for (auto x : G[v]) tG.push_back(x);
        }
      }
      if (t && flag == 2) return fail = 4, 0;
      if (t == 1) reverse(tG.begin(), tG.end());
      G[u] = tG;
      return u;
    }
  }
  void dfs_permutation(int u, vector<int> &per) {
    if (u <= n) per.push_back(u);
    for (auto v : G[u]) dfs_permutation(v, per);
  }
  vector<int> get_permutation() {
    vector<int> res;
    dfs_permutation(n + 1, res);
    return res;
  }
  void restrict(vector<int> res) {
    for (int i = 1; i <= n; i++) s[i] = 0;
    for (auto x : res) s[x] = 1;
    dfs(n + 1);
    check(n + 1, 0);
  }
};
void work() {
  int n;
  cin >> n;
  PQ_tree *pq = new PQ_tree;
  pq->init(n);
  vector<string> s(n);
  for (int i = 0; i < n; i++) {
    cin >> s[i];
    vector<int> res;
    for (int j = 0; j < n; j++)
      if (s[i][j] == '1') res.push_back(j + 1);
    pq->restrict(res);
  }
  if (pq->fail) {
    cout << "NO" << endl;
  } else {
    cout << "YES" << endl;
    vector<int> perm = pq->get_permutation();
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) cout << s[i][perm[j] - 1];
      cout << endl;
    }
  }
  delete pq;
}
int main(int argc, char **argv) {
  int tc = 1;
  for (int ca = 1; ca <= tc; ca++) {
    work();
  }
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

Let's consider an n × n square matrix, consisting of digits one and zero.

We'll consider a matrix good, if it meets the following condition: in each row of the matrix all ones go in one group. That is, each row of the matrix looks like that 00...0011...1100...00 (or simply consists of zeroes if it has no ones).

You are given matrix a of size n × n, consisting of zeroes and ones. Your task is to determine whether you can get a good matrix b from it by rearranging the columns or not.

Input

The first line contains integer n (1 ≤ n ≤ 500) — the size of matrix a.

Each of n following lines contains n characters "0" and "1" — matrix a. Note that the characters are written without separators.

Output

Print "YES" in the first line, if you can rearrange the matrix columns so as to get a good matrix b. In the next n lines print the good matrix b. If there are multiple answers, you are allowed to print any of them.

If it is impossible to get a good matrix, print "NO".

Examples

Input

6
100010
110110
011001
010010
000100
011001


Output

YES
011000
111100
000111
001100
100000
000111


Input

3
110
101
011


Output

NO

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline void read(T &x) {
  static char _c;
  static bool _f;
  x = 0;
  _f = 0;
  _c = getchar();
  while (_c < '0' || '9' < _c) {
    if (_c == '-') _f = true;
    _c = getchar();
  }
  while ('0' <= _c && _c <= '9') {
    x = (x << 1) + (x << 3) + (_c & 15);
    _c = getchar();
  }
  if (_f) x = -x;
}
template <typename T>
inline void Min(T &x, T y) {
  if (y < x) x = y;
}
template <typename T>
inline void Max(T &x, T y) {
  if (x < y) x = y;
}
const int INF = 0x3f3f3f3f;
const double pi = (double)acos(-1.0);
const double eps = (double)1e-8;
const int e5 = (int)1e5 + 5;
const int MOD = (int)1e9 + 7;
inline int sig(double x) { return x < -eps ? -1 : eps < x; }
long long fp(long long a, long long n, long long mod = MOD) {
  if (n < 0) a = fp(a, mod - 2, mod), n = -n;
  long long res = 1;
  for (; n; n >>= 1, a = a * a % mod)
    if (n & 1) res = res * a % mod;
  return res;
}
struct Mint {
  int x;
  Mint() { x = 0; }
  Mint(int _x) : x(_x) {
    if (x < 0 || x >= MOD) x = (x % MOD + MOD) % MOD;
  }
  Mint(long long _x) : x(_x) {
    if (x < 0 || x >= MOD) x = (x % MOD + MOD) % MOD;
  }
  Mint operator-() const { return Mint(MOD - x); }
  Mint operator+(const Mint &rhs) const {
    return Mint(x + rhs.x >= MOD ? x + rhs.x - MOD : x + rhs.x);
  }
  Mint operator-(const Mint &rhs) const {
    return Mint(x - rhs.x < 0 ? x - rhs.x + MOD : x - rhs.x);
  }
  Mint operator*(const Mint &rhs) const {
    return Mint((long long)x * rhs.x % MOD);
  }
  Mint operator/(const Mint &rhs) const {
    return Mint(x * fp(rhs.x, -1) % MOD);
  }
  Mint &operator+=(const Mint &rhs) {
    x += rhs.x;
    if (x >= MOD) x -= MOD;
    return *this;
  }
  Mint &operator*=(const Mint &rhs) {
    x = ((long long)x * rhs.x) % MOD;
    return *this;
  }
  bool operator==(const Mint &rhs) const { return x == rhs.x; }
  bool operator!=(const Mint &rhs) const { return x != rhs.x; }
  friend ostream &operator<<(ostream &out, const Mint &rhs) {
    return out << rhs.x;
  }
  friend istream &operator>>(istream &in, Mint &rhs) { return in >> rhs.x; }
};
const int maxn = (int)2e5 + 20;
const int maxm = (int)1e6 + 20;
const int N = 500 + 5;
struct PQ_tree {
  int n, tot;
  int fail;
  vector<int> G[N << 2];
  int ty[N << 2];
  int sz[N << 2];
  int szc[N << 2];
  bool s[N];
  inline int getstate(int u) {
    if (szc[u] == 0) return 0;
    if (szc[u] == sz[u]) return 2;
    return 1;
  }
  void addson(int x, int y) {
    if (y) G[x].push_back(y);
  }
  void join(int x, int y) {
    for (auto v : G[y]) G[x].push_back(v);
  }
  int mergeP(vector<int> &vec) {
    if (vec.size() == 0) return 0;
    if (vec.size() == 1) return vec[0];
    G[++tot] = vec;
    return tot;
  }
  void init(int _n) {
    n = _n;
    tot = n + 1;
    memset(ty, 0, sizeof(ty));
    for (int i = 1; i <= n; i++) G[n + 1].push_back(i);
    fail = 0;
  }
  void dfs(int u) {
    sz[u] = u <= n;
    szc[u] = u <= n && s[u];
    for (auto v : G[u]) {
      dfs(v);
      sz[u] += sz[v];
      szc[u] += szc[v];
    }
  }
  int check(int u, int t) {
    if (fail) return 0;
    vector<int> vec[3];
    for (auto v : G[u]) vec[getstate(v)].push_back(v);
    if (vec[1].size() > 2 || (t && vec[1].size() > 1)) return fail = 1, 0;
    if (t == 0 && vec[1].size() == 1 && vec[2].size() == 0)
      return check(vec[1][0], 0);
    if (ty[u] == 0) {
      int p2 = mergeP(vec[2]);
      if (t == 0) {
        G[u] = vec[0];
        if (vec[1].size() == 0)
          addson(u, p2);
        else {
          int tmp1 = check(vec[1][0], 2);
          addson(tmp1, p2);
          if (vec[1].size() == 2) join(tmp1, check(vec[1][1], 1));
          addson(u, tmp1);
        }
        return u;
      } else {
        ty[u] = 1;
        G[u].clear();
        addson(u, p2);
        if (vec[1].size() == 1) join(u, check(vec[1][0], 1));
        addson(u, mergeP(vec[0]));
        if (t == 2) reverse(G[u].begin(), G[u].end());
      }
      return u;
    } else {
      if (getstate(G[u].front()) > getstate(G[u].back()))
        reverse(G[u].begin(), G[u].end());
      int flag = 0;
      vector<int> tG;
      for (auto v : G[u]) {
        int sta = getstate(v);
        if (sta == 0) {
          if (flag == 1) flag = 2;
          tG.push_back(v);
        } else if (sta == 2) {
          if (flag == 0)
            flag = 1;
          else if (flag == 2)
            return fail = 2, 0;
          tG.push_back(v);
        } else {
          int p1;
          if (flag == 0)
            flag = 1, p1 = check(v, 2);
          else if (flag == 1)
            flag = 2, p1 = check(v, 1);
          else
            return fail = 3, 0;
          for (auto x : G[v]) tG.push_back(x);
        }
      }
      if (t && flag == 2) return fail = 4, 0;
      if (t == 1) reverse(tG.begin(), tG.end());
      G[u] = tG;
      return u;
    }
  }
  void dfs_permutation(int u, vector<int> &per) {
    if (u <= n) per.push_back(u);
    for (auto v : G[u]) dfs_permutation(v, per);
  }
  vector<int> get_permutation() {
    vector<int> res;
    dfs_permutation(n + 1, res);
    return res;
  }
  void restrict(vector<int> res) {
    for (int i = 1; i <= n; i++) s[i] = 0;
    for (auto x : res) s[x] = 1;
    dfs(n + 1);
    check(n + 1, 0);
  }
};
void work() {
  int n;
  cin >> n;
  PQ_tree *pq = new PQ_tree;
  pq->init(n);
  vector<string> s(n);
  for (int i = 0; i < n; i++) {
    cin >> s[i];
    vector<int> res;
    for (int j = 0; j < n; j++)
      if (s[i][j] == '1') res.push_back(j + 1);
    pq->restrict(res);
  }
  if (pq->fail) {
    cout << "NO" << endl;
  } else {
    cout << "YES" << endl;
    vector<int> perm = pq->get_permutation();
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) cout << s[i][perm[j] - 1];
      cout << endl;
    }
  }
  delete pq;
}
int main(int argc, char **argv) {
  int tc = 1;
  for (int ca = 1; ca <= tc; ca++) {
    work();
  }
  return 0;
}

```