#include <bits/stdc++.h>
using namespace std;
const int N = 1000 + 5;
struct Tree {
  bool tp;
  int fa;
  deque<int> c[2];
  deque<int>::iterator pfa[2];
} tr[N << 1];
int n, root, top, answer, rem[N << 1], ans[N], q[N << 1];
int tp[N << 1], sum[N << 1], tot[N << 1];
char st[N][N];
inline void remain(int now) { rem[++top] = now; }
inline int getrem(void) {
  int now = rem[top--];
  tr[now].c[0].clear();
  ;
  tr[now].c[1].clear();
  ;
  return now;
}
inline void addsonbg(int now, int ch) {
  tr[ch].fa = now;
  tr[now].c[0].push_front(ch);
  tr[ch].pfa[0] = tr[now].c[0].begin();
  tr[now].c[1].push_back(ch);
  tr[ch].pfa[1] = tr[now].c[1].end() - 1;
}
inline void addsoned(int now, int ch) {
  tr[ch].fa = now;
  tr[now].c[0].push_back(ch);
  tr[ch].pfa[0] = tr[now].c[0].end() - 1;
  tr[now].c[1].push_front(ch);
  tr[ch].pfa[1] = tr[now].c[1].begin();
}
inline void changeson(int x, int y) {
  tp[y] = tp[x];
  tot[y] = tot[x];
  sum[y] = sum[x];
  tr[y].pfa[0] = tr[x].pfa[0];
  tr[y].pfa[1] = tr[x].pfa[1];
  if (tr[y].fa = tr[x].fa)
    *(tr[y].pfa[0]) = *(tr[y].pfa[1]) = y;
  else
    root = y;
}
inline void init(int n) {
  tr[root = n + 1].tp = 0;
  for (int i = N - 1; i > root; --i) rem[++top] = i;
  for (int i = 1; i <= n; ++i) addsoned(root, i);
}
inline bool reduce(char *st) {
  memset(tp, -1, sizeof tp);
  memset(sum, 0, sizeof sum);
  memset(tot, 0, sizeof tot);
  int l, r, cnt = 0, now, ff;
  vector<int> ch[3];
  bool isroot;
  for (int i = 1; i <= n; ++i)
    if (tp[i] = (st[i] == '1')) sum[q[++cnt] = i] = 1;
  l = 1;
  r = cnt;
  for (int i = 1; i <= n; ++i)
    if (!tp[i]) q[++r] = i;
  for (; l <= r; ++l) {
    isroot = (sum[now = q[l]] == cnt);
    ff = tr[now].fa;
    if (tp[now] == 2) {
      ch[0].clear();
      ;
      ch[1].clear();
      ;
      ch[2].clear();
      ;
      if (!tr[now].tp) {
        for (deque<int>::iterator it = tr[now].c[0].begin();
             it != tr[now].c[0].end(); ++it)
          ch[tp[*it]].push_back(*it);
        tr[now].c[0].clear();
        ;
        tr[now].c[1].clear();
        ;
        if (ch[2].empty()) {
          if (!isroot && ch[0].size() > 1) {
            int tmp = getrem();
            for (vector<int>::iterator it = ch[0].begin(); it != ch[0].end();
                 ++it)
              addsoned(tmp, *it);
            tr[tmp].tp = 0;
            addsoned(now, tmp);
          } else
            for (vector<int>::iterator it = ch[0].begin(); it != ch[0].end();
                 ++it)
              addsoned(now, *it);
          if (ch[1].size() > 1) {
            int tmp = getrem();
            for (vector<int>::iterator it = ch[1].begin(); it != ch[1].end();
                 ++it)
              addsoned(tmp, *it);
            tr[tmp].tp = 0;
            addsoned(now, tmp);
          } else if (ch[1].size() == 1)
            addsoned(now, ch[1][0]);
        } else if (ch[2].size() == 1) {
          int p1 = ch[2][0];
          tr[p1].tp = 1;
          if (isroot) {
            if (ch[1].size() > 1) {
              int tmp = getrem();
              for (vector<int>::iterator it = ch[1].begin(); it != ch[1].end();
                   ++it)
                addsoned(tmp, *it);
              tr[tmp].tp = 0;
              addsoned(p1, tmp);
            } else if (ch[1].size() == 1)
              addsoned(p1, ch[1][0]);
            if (!ch[0].empty()) {
              for (vector<int>::iterator it = ch[0].begin(); it != ch[0].end();
                   ++it)
                addsoned(now, *it);
              addsoned(now, p1);
            } else
              changeson(now, p1), remain(now), now = p1;
          } else {
            if (ch[1].size() > 1) {
              int tmp = getrem();
              for (vector<int>::iterator it = ch[1].begin(); it != ch[1].end();
                   ++it)
                addsoned(tmp, *it);
              tr[tmp].tp = 0;
              addsoned(p1, tmp);
            } else if (ch[1].size() == 1)
              addsoned(p1, ch[1][0]);
            if (ch[0].size() > 1) {
              int tmp = getrem();
              for (vector<int>::iterator it = ch[0].begin(); it != ch[0].end();
                   ++it)
                addsoned(tmp, *it);
              tr[tmp].tp = 0;
              addsonbg(p1, tmp);
            } else if (ch[0].size() == 1)
              addsonbg(p1, ch[0][0]);
            changeson(now, p1);
            remain(now);
            now = p1;
          }
        } else {
          if (ch[2].size() > 2 || !isroot) return 1;
          int p1 = ch[2][0], p2 = ch[2][1], tmp = getrem();
          for (deque<int>::iterator it = tr[p1].c[0].begin();
               it != tr[p1].c[0].end(); ++it)
            addsoned(tmp, *it);
          if (ch[1].size() > 1) {
            int nd = getrem();
            for (vector<int>::iterator it = ch[1].begin(); it != ch[1].end();
                 ++it)
              addsoned(nd, *it);
            tr[nd].tp = 0;
            addsoned(tmp, nd);
          } else if (ch[1].size() == 1)
            addsoned(tmp, ch[1][0]);
          for (deque<int>::iterator it = tr[p2].c[1].begin();
               it != tr[p2].c[1].end(); ++it)
            addsoned(tmp, *it);
          remain(p1);
          remain(p2);
          tr[tmp].tp = 1;
          if (!ch[0].empty()) {
            for (vector<int>::iterator it = ch[0].begin(); it != ch[0].end();
                 ++it)
              addsoned(now, *it);
            addsoned(now, tmp);
          } else
            changeson(now, tmp), remain(now), now = tmp;
        }
      } else {
        deque<int>::iterator le, ri;
        for (le = tr[now].c[0].begin(); !tp[*le]; ++le)
          ;
        for (ri = le; ri != tr[now].c[0].end() - 1 && tp[*(ri + 1)] == 1; ++ri)
          ;
        if (ri != tr[now].c[0].end() - 1 && tp[*(ri + 1)] == 2) ++ri;
        for (deque<int>::iterator it = ri + 1; it != tr[now].c[0].end(); ++it)
          if (tp[*it]) return 1;
        int l = *le, r = *ri;
        bool lnkle, lnkri;
        lnkle = !(le != tr[now].c[0].begin() || tp[l] == 2);
        lnkri = !(ri != tr[now].c[0].end() - 1 || tp[r] == 2);
        if (!isroot && !lnkle && !lnkri) {
          if (le != ri ||
              (le != tr[now].c[0].begin() && ri != tr[now].c[0].end() - 1))
            return 1;
          if (le == tr[now].c[0].begin() && tp[l] == 2) goto flagr;
          if (ri == tr[now].c[0].end() - 1 && tp[r] == 2) goto flagl;
        }
        if (tp[l] == 2 && tp[r] == 2) {
          tr[l].tp = 1;
          if (le != ri)
            for (deque<int>::iterator it = le + 1; it != ri; ++it)
              addsoned(l, *it);
          for (deque<int>::iterator it = tr[r].c[1].begin();
               it != tr[r].c[1].end(); ++it)
            addsoned(l, *it);
          remain(r);
          for (deque<int>::iterator it = le; it != tr[now].c[0].begin(); --it)
            addsonbg(l, *(it - 1));
          for (deque<int>::iterator it = ri + 1; it != tr[now].c[0].end(); ++it)
            addsoned(l, *it);
          changeson(now, l);
          remain(now);
          now = l;
        } else if (tp[l] == 2) {
        flagl:;
          tr[l].tp = 1;
          for (deque<int>::iterator it = le; it != tr[now].c[0].begin(); --it)
            addsonbg(l, *(it - 1));
          for (deque<int>::iterator it = le + 1; it != tr[now].c[0].end(); ++it)
            addsoned(l, *it);
          changeson(now, l);
          remain(now);
          now = l;
        } else if (tp[r] == 2) {
        flagr:;
          tr[r].tp = 1;
          for (deque<int>::iterator it = ri + 1; it != tr[now].c[0].end(); ++it)
            addsonbg(r, *it);
          for (deque<int>::iterator it = ri; it != tr[now].c[0].begin(); --it)
            addsoned(r, *(it - 1));
          changeson(now, r);
          remain(now);
          now = r;
        } else {
          if (!isroot && ri != tr[now].c[0].end() - 1)
            swap(tr[now].c[0], tr[now].c[1]);
        }
      }
    }
    if (isroot) break;
    sum[ff] += sum[now];
    if (!~tp[ff])
      tp[ff] = tp[now];
    else if (tp[ff] != tp[now])
      tp[ff] = 2;
    if (++tot[ff] == tr[ff].c[0].size()) q[++r] = ff;
  }
  return 0;
}
inline void display(int now) {
  if (tr[now].c[0].empty()) {
    ans[++answer] = now;
    return;
  }
  for (deque<int>::iterator it = tr[now].c[0].begin(); it != tr[now].c[0].end();
       ++it)
    display(*it);
}
int main(int argc, char **argv) {
  scanf("%d", &n);
  init(n);
  for (int i = 1; i <= n; ++i) {
    scanf("%s", st[i] + 1);
    if (reduce(st[i])) {
      puts("NO");
      return 0;
    }
  }
  puts("YES");
  display(root);
  for (int i = 1; i <= n; ++i) {
    for (int j = 1; j <= n; ++j) putchar(st[i][ans[j]]);
    puts("");
  }
  return 0;
}

### Prompt

Create a solution in CPP for the following problem:

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;
const int N = 1000 + 5;
struct Tree {
  bool tp;
  int fa;
  deque<int> c[2];
  deque<int>::iterator pfa[2];
} tr[N << 1];
int n, root, top, answer, rem[N << 1], ans[N], q[N << 1];
int tp[N << 1], sum[N << 1], tot[N << 1];
char st[N][N];
inline void remain(int now) { rem[++top] = now; }
inline int getrem(void) {
  int now = rem[top--];
  tr[now].c[0].clear();
  ;
  tr[now].c[1].clear();
  ;
  return now;
}
inline void addsonbg(int now, int ch) {
  tr[ch].fa = now;
  tr[now].c[0].push_front(ch);
  tr[ch].pfa[0] = tr[now].c[0].begin();
  tr[now].c[1].push_back(ch);
  tr[ch].pfa[1] = tr[now].c[1].end() - 1;
}
inline void addsoned(int now, int ch) {
  tr[ch].fa = now;
  tr[now].c[0].push_back(ch);
  tr[ch].pfa[0] = tr[now].c[0].end() - 1;
  tr[now].c[1].push_front(ch);
  tr[ch].pfa[1] = tr[now].c[1].begin();
}
inline void changeson(int x, int y) {
  tp[y] = tp[x];
  tot[y] = tot[x];
  sum[y] = sum[x];
  tr[y].pfa[0] = tr[x].pfa[0];
  tr[y].pfa[1] = tr[x].pfa[1];
  if (tr[y].fa = tr[x].fa)
    *(tr[y].pfa[0]) = *(tr[y].pfa[1]) = y;
  else
    root = y;
}
inline void init(int n) {
  tr[root = n + 1].tp = 0;
  for (int i = N - 1; i > root; --i) rem[++top] = i;
  for (int i = 1; i <= n; ++i) addsoned(root, i);
}
inline bool reduce(char *st) {
  memset(tp, -1, sizeof tp);
  memset(sum, 0, sizeof sum);
  memset(tot, 0, sizeof tot);
  int l, r, cnt = 0, now, ff;
  vector<int> ch[3];
  bool isroot;
  for (int i = 1; i <= n; ++i)
    if (tp[i] = (st[i] == '1')) sum[q[++cnt] = i] = 1;
  l = 1;
  r = cnt;
  for (int i = 1; i <= n; ++i)
    if (!tp[i]) q[++r] = i;
  for (; l <= r; ++l) {
    isroot = (sum[now = q[l]] == cnt);
    ff = tr[now].fa;
    if (tp[now] == 2) {
      ch[0].clear();
      ;
      ch[1].clear();
      ;
      ch[2].clear();
      ;
      if (!tr[now].tp) {
        for (deque<int>::iterator it = tr[now].c[0].begin();
             it != tr[now].c[0].end(); ++it)
          ch[tp[*it]].push_back(*it);
        tr[now].c[0].clear();
        ;
        tr[now].c[1].clear();
        ;
        if (ch[2].empty()) {
          if (!isroot && ch[0].size() > 1) {
            int tmp = getrem();
            for (vector<int>::iterator it = ch[0].begin(); it != ch[0].end();
                 ++it)
              addsoned(tmp, *it);
            tr[tmp].tp = 0;
            addsoned(now, tmp);
          } else
            for (vector<int>::iterator it = ch[0].begin(); it != ch[0].end();
                 ++it)
              addsoned(now, *it);
          if (ch[1].size() > 1) {
            int tmp = getrem();
            for (vector<int>::iterator it = ch[1].begin(); it != ch[1].end();
                 ++it)
              addsoned(tmp, *it);
            tr[tmp].tp = 0;
            addsoned(now, tmp);
          } else if (ch[1].size() == 1)
            addsoned(now, ch[1][0]);
        } else if (ch[2].size() == 1) {
          int p1 = ch[2][0];
          tr[p1].tp = 1;
          if (isroot) {
            if (ch[1].size() > 1) {
              int tmp = getrem();
              for (vector<int>::iterator it = ch[1].begin(); it != ch[1].end();
                   ++it)
                addsoned(tmp, *it);
              tr[tmp].tp = 0;
              addsoned(p1, tmp);
            } else if (ch[1].size() == 1)
              addsoned(p1, ch[1][0]);
            if (!ch[0].empty()) {
              for (vector<int>::iterator it = ch[0].begin(); it != ch[0].end();
                   ++it)
                addsoned(now, *it);
              addsoned(now, p1);
            } else
              changeson(now, p1), remain(now), now = p1;
          } else {
            if (ch[1].size() > 1) {
              int tmp = getrem();
              for (vector<int>::iterator it = ch[1].begin(); it != ch[1].end();
                   ++it)
                addsoned(tmp, *it);
              tr[tmp].tp = 0;
              addsoned(p1, tmp);
            } else if (ch[1].size() == 1)
              addsoned(p1, ch[1][0]);
            if (ch[0].size() > 1) {
              int tmp = getrem();
              for (vector<int>::iterator it = ch[0].begin(); it != ch[0].end();
                   ++it)
                addsoned(tmp, *it);
              tr[tmp].tp = 0;
              addsonbg(p1, tmp);
            } else if (ch[0].size() == 1)
              addsonbg(p1, ch[0][0]);
            changeson(now, p1);
            remain(now);
            now = p1;
          }
        } else {
          if (ch[2].size() > 2 || !isroot) return 1;
          int p1 = ch[2][0], p2 = ch[2][1], tmp = getrem();
          for (deque<int>::iterator it = tr[p1].c[0].begin();
               it != tr[p1].c[0].end(); ++it)
            addsoned(tmp, *it);
          if (ch[1].size() > 1) {
            int nd = getrem();
            for (vector<int>::iterator it = ch[1].begin(); it != ch[1].end();
                 ++it)
              addsoned(nd, *it);
            tr[nd].tp = 0;
            addsoned(tmp, nd);
          } else if (ch[1].size() == 1)
            addsoned(tmp, ch[1][0]);
          for (deque<int>::iterator it = tr[p2].c[1].begin();
               it != tr[p2].c[1].end(); ++it)
            addsoned(tmp, *it);
          remain(p1);
          remain(p2);
          tr[tmp].tp = 1;
          if (!ch[0].empty()) {
            for (vector<int>::iterator it = ch[0].begin(); it != ch[0].end();
                 ++it)
              addsoned(now, *it);
            addsoned(now, tmp);
          } else
            changeson(now, tmp), remain(now), now = tmp;
        }
      } else {
        deque<int>::iterator le, ri;
        for (le = tr[now].c[0].begin(); !tp[*le]; ++le)
          ;
        for (ri = le; ri != tr[now].c[0].end() - 1 && tp[*(ri + 1)] == 1; ++ri)
          ;
        if (ri != tr[now].c[0].end() - 1 && tp[*(ri + 1)] == 2) ++ri;
        for (deque<int>::iterator it = ri + 1; it != tr[now].c[0].end(); ++it)
          if (tp[*it]) return 1;
        int l = *le, r = *ri;
        bool lnkle, lnkri;
        lnkle = !(le != tr[now].c[0].begin() || tp[l] == 2);
        lnkri = !(ri != tr[now].c[0].end() - 1 || tp[r] == 2);
        if (!isroot && !lnkle && !lnkri) {
          if (le != ri ||
              (le != tr[now].c[0].begin() && ri != tr[now].c[0].end() - 1))
            return 1;
          if (le == tr[now].c[0].begin() && tp[l] == 2) goto flagr;
          if (ri == tr[now].c[0].end() - 1 && tp[r] == 2) goto flagl;
        }
        if (tp[l] == 2 && tp[r] == 2) {
          tr[l].tp = 1;
          if (le != ri)
            for (deque<int>::iterator it = le + 1; it != ri; ++it)
              addsoned(l, *it);
          for (deque<int>::iterator it = tr[r].c[1].begin();
               it != tr[r].c[1].end(); ++it)
            addsoned(l, *it);
          remain(r);
          for (deque<int>::iterator it = le; it != tr[now].c[0].begin(); --it)
            addsonbg(l, *(it - 1));
          for (deque<int>::iterator it = ri + 1; it != tr[now].c[0].end(); ++it)
            addsoned(l, *it);
          changeson(now, l);
          remain(now);
          now = l;
        } else if (tp[l] == 2) {
        flagl:;
          tr[l].tp = 1;
          for (deque<int>::iterator it = le; it != tr[now].c[0].begin(); --it)
            addsonbg(l, *(it - 1));
          for (deque<int>::iterator it = le + 1; it != tr[now].c[0].end(); ++it)
            addsoned(l, *it);
          changeson(now, l);
          remain(now);
          now = l;
        } else if (tp[r] == 2) {
        flagr:;
          tr[r].tp = 1;
          for (deque<int>::iterator it = ri + 1; it != tr[now].c[0].end(); ++it)
            addsonbg(r, *it);
          for (deque<int>::iterator it = ri; it != tr[now].c[0].begin(); --it)
            addsoned(r, *(it - 1));
          changeson(now, r);
          remain(now);
          now = r;
        } else {
          if (!isroot && ri != tr[now].c[0].end() - 1)
            swap(tr[now].c[0], tr[now].c[1]);
        }
      }
    }
    if (isroot) break;
    sum[ff] += sum[now];
    if (!~tp[ff])
      tp[ff] = tp[now];
    else if (tp[ff] != tp[now])
      tp[ff] = 2;
    if (++tot[ff] == tr[ff].c[0].size()) q[++r] = ff;
  }
  return 0;
}
inline void display(int now) {
  if (tr[now].c[0].empty()) {
    ans[++answer] = now;
    return;
  }
  for (deque<int>::iterator it = tr[now].c[0].begin(); it != tr[now].c[0].end();
       ++it)
    display(*it);
}
int main(int argc, char **argv) {
  scanf("%d", &n);
  init(n);
  for (int i = 1; i <= n; ++i) {
    scanf("%s", st[i] + 1);
    if (reduce(st[i])) {
      puts("NO");
      return 0;
    }
  }
  puts("YES");
  display(root);
  for (int i = 1; i <= n; ++i) {
    for (int j = 1; j <= n; ++j) putchar(st[i][ans[j]]);
    puts("");
  }
  return 0;
}

```