You have matrix a of size n × n. Let's number the rows of the matrix from 1 to n from top to bottom, let's number the columns from 1 to n from left to right. Let's use aij to represent the element on the intersection of the i-th row and the j-th column. 

Matrix a meets the following two conditions: 

  * for any numbers i, j (1 ≤ i, j ≤ n) the following inequality holds: aij ≥ 0; 
  * <image>. 



Matrix b is strictly positive, if for any numbers i, j (1 ≤ i, j ≤ n) the inequality bij > 0 holds. You task is to determine if there is such integer k ≥ 1, that matrix ak is strictly positive.

Input

The first line contains integer n (2 ≤ n ≤ 2000) — the number of rows and columns in matrix a.

The next n lines contain the description of the rows of matrix a. The i-th line contains n non-negative integers ai1, ai2, ..., ain (0 ≤ aij ≤ 50). It is guaranteed that <image>.

Output

If there is a positive integer k ≥ 1, such that matrix ak is strictly positive, print "YES" (without the quotes). Otherwise, print "NO" (without the quotes). 

Examples

Input

2
1 0
0 1


Output

NO


Input

5
4 5 6 1 2
1 2 3 4 5
6 4 1 2 4
1 1 1 1 1
4 4 4 4 4


Output

YES
#include <bits/stdc++.h>
using namespace std;
namespace IO {
void setIn(string s) { freopen(s.c_str(), "r", stdin); }
void setOut(string s) { freopen(s.c_str(), "w", stdout); }
void setIO(string s = "") {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin.exceptions(cin.failbit);
  if (s.size()) {
    setIn(s + ".inp");
    setOut(s + ".out");
  } else {
  }
}
}  // namespace IO
using namespace IO;
namespace Function {
template <typename T1, typename T2>
void amax(T1 &a, T2 b) {
  if (typeid(a).name() == typeid(int).name() &&
      typeid(b).name() == typeid(long long).name()) {
    cout << "Error on amax";
    exit(0);
  }
  if (a < b) a = b;
}
template <typename T1, typename T2>
void amin(T1 &a, T2 b) {
  if (a > b) a = b;
}
template <typename T>
void compress(vector<T> &a) {
  sort(a.begin(), a.end());
  a.resize(unique(a.begin(), a.end()) - a.begin());
}
template <typename T>
long long sqr(T x) {
  return 1LL * x * x;
}
template <typename T1, typename T2>
long long gcd(T1 a, T2 b) {
  return (b == 0 ? a : gcd(b, a % b));
}
template <typename T1, typename T2>
long long lcm(T1 a, T2 b) {
  return 1LL * a / gcd(a, b) * b;
}
}  // namespace Function
using namespace Function;
namespace Output {
void print(int x) { cout << x << "\n"; }
void print(unsigned int x) { cout << x << "\n"; }
void print(long unsigned int x) { cout << x << "\n"; }
void print(long long x) { cout << x << "\n"; }
void print(unsigned long long x) { cout << x << "\n"; }
void print(float x) { cout << x << "\n"; }
void print(double x) { cout << x << "\n"; }
void print(long double x) { cout << x << "\n"; }
void print(char x) { cout << x << "\n"; }
void print(const char *x) { cout << x << "\n"; }
void print(string x) { cout << x << "\n"; }
void print(bool x) { cout << x << "\n"; }
template <class T, class... Ts>
void print(T t, Ts... ts) {
  cout << t << " ";
  print(ts...);
}
template <typename T1, typename T2>
void print(pair<T1, T2> a) {
  print(a.first, a.second);
}
template <typename T>
void print(T a) {
  for (auto it : a) {
    print(it);
  }
}
template <class T, class... Ts>
void prine(T t, Ts... ts) {
  print(t, ts...);
  exit(0);
}
}  // namespace Output
using namespace Output;
const int dx[] = {1, -1, 0, 0};
const int dy[] = {0, 0, 1, -1};
const int INF = 1e9;
const long long INFL = 1e18;
const int MOD = 1e9 + 7;
const int N = 2e3 + 10;
bool vis[N];
bool a[N][N];
int n;
int cnt[N];
void dfs(int u) {
  vis[u] = 1;
  cnt[u]++;
  for (int i = 0; i < n; i++) {
    if (a[u][i] && !vis[i]) {
      dfs(i);
    }
  }
}
int main() {
  setIO();
  cin >> n;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      int x;
      cin >> x;
      a[i][j] = (x > 0);
    }
  }
  dfs(1);
  memset(vis, 0, sizeof(vis));
  for (int i = 1; i < n; i++) {
    for (int j = 0; j < i; j++) {
      swap(a[i][j], a[j][i]);
    }
  }
  dfs(1);
  for (int i = 0; i < n; i++) {
    if (cnt[i] != 2) {
      prine("NO");
    }
  }
  print("YES");
  return 0;
}
