Problem: You have a cross-section paper with W x H squares, and each of them is painted either in white or black. You want to re-arrange the squares into a neat checkered pattern, in which black and white squares are arranged alternately both in horizontal and vertical directions (the figure shown below is a checkered patter with W = 5 and H = 5). To achieve this goal, you can perform the following two operations as many times you like in an arbitrary sequence: swapping of two arbitrarily chosen columns, and swapping of two arbitrarily chosen rows.

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Create a program to determine, starting from the given cross-section paper, if you can re-arrange them into a checkered pattern.



Input

The input is given in the following format.


W H
c1,1 c1,2 ... c1,W
c2,1 c2,2 ... c2,W
:
cH,1 cH,2 ... cH,W


The first line provides the number of squares in horizontal direction W (2≤W≤1000) and those in vertical direction H(2≤H≤1000). Each of subsequent H lines provides an array of W integers ci,j corresponding to a square of i-th row and j-th column. The color of the square is white if ci,j is 0, and black if it is 1.

Output

Output "yes" if the goal is achievable and "no" otherwise.

Examples

Input

3 2
1 1 0
0 0 1


Output

yes


Input

2 2
0 0
1 1


Output

no

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

#define fs first
#define sc second
#define pb emplace_back
#define mp make_pair
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()

const int32_t inf = 1001001001;
const int64_t infll = 1001001001001001001ll;
const int dx[] = {0, -1, 1, 0, -1, 1, -1, 1}, dy[] = {-1, 0, 0, 1, -1, -1, 1, 1};

template <typename T> using vector2d = vector<vector<T>>;

// clang-format off
template <typename T> void sort(vector<T> &v) { sort(all(v)); }
// ostream &operator<<(ostream &os, __int128_t value) { if (ostream::sentry(os)) { __uint128_t tmp = value < 0 ? -value : value; char buffer[64]; char *d = end(buffer); do { --d; *d = "0123456789"[tmp % 10]; tmp /= 10; } while (tmp != 0); if (value < 0) { --d; *d = '-'; } int len = end(buffer) - d; if (os.rdbuf()->sputn(d, len) != len) { os.setstate(ios_base::badbit); }} return os; }
// istream &operator>>(istream &is, __int128_t &value) { string in; is >> in; value = 0; for (const char &c : in) { if ('0' <= c && c <= '9') value = 10 * value + (c - '0'); } if (in[0] == '-') value *= -1; return is; }
// ostream &operator<<(ostream &os, __uint128_t value) { if (ostream::sentry(os)) { char buffer[64]; char *d = end(buffer); do { --d; *d = "0123456789"[value % 10]; value /= 10; } while (value != 0); int len = end(buffer) - d; if (os.rdbuf()->sputn(d, len) != len) { os.setstate(ios_base::badbit); }} return os; }
// istream &operator>>(istream &is, __uint128_t &value) { string in; is >> in; value = 0; for (const char &c : in) { if ('0' <= c && c <= '9') value = 10 * value + (c - '0'); } return is; }
template <typename T> ostream &operator<<(ostream &os, vector<T> &v) { os << v[0]; for (int i = 1; i < v.size(); ++i) os << " " << v[i]; return os; }
template <typename T> istream &operator>>(istream &is, vector<T> &v) { for (T &in : v) is >> in; return is; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, pair<T1, T2> p) { os << p.fs << " " << p.sc; return os; }
template <typename T1, typename T2> istream &operator>>(istream &is, pair<T1, T2> &p) { is >> p.fs >> p.sc; return is; }

struct IoSetup { IoSetup(){ cin.tie(0); ios::sync_with_stdio(0); cout << fixed << setprecision(10); cerr << fixed << setprecision(10); } } iosetup;

inline int64_t in() { int64_t x = 0; cin >> x; return x; }
template <typename T1, typename T2> inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }
template <typename T1, typename T2> inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }
// clang-format on

signed main(int argc, char *argv[]) {
  int w = in(), h = in();
  char c[1000][1000];

  for (int i = 0; i < h; ++i) {
    for (int j = 0; j < w; ++j) {
      cin >> c[i][j];
    }
  }

  set<string> st1, st2;
  for (int i = 0; i < h; ++i) {
    string s;
    for (int j = 0; j < w; ++j) {
      s += c[i][j];
    }

    st1.insert(s);
    // cerr << s << endl;
  }

  for (int j = 0; j < w; ++j) {
    string s;
    for (int i = 0; i < h; ++i) {
      s += c[i][j];
    }

    st2.insert(s);
  }

  // cerr << st1.count(*st1.begin()) << endl;
  // cerr << st1.count(*st1.rbegin()) << endl;

  auto izryt = [&](set<string> &st) {
    return (st.size() == 2 && abs(int(st.count(*st.begin())) - int(st.count(*st.rbegin()))) <= 1);
  };

  if (izryt(st1) && izryt(st2))
    cout << "yes" << endl;
  else
    cout << "no" << endl;
}