//#include <bits/stdc++.h>

#include <iostream>
#include <algorithm>

#include <bitset>
#include <vector>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <stack>
#include <queue>
#include <deque>
#include <cstring>
#include <string>
#include <utility>
#include <array>
#include <complex>
#include <valarray>

#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
#include <chrono>
#include <random>
#include <numeric>

#include<memory>


using namespace std;
#define int long long

typedef long long ll;
typedef unsigned long long ull;
//typedef unsigned __int128 HASH;
typedef pair<int,int> pii;
typedef pair<ll, ll> pll;
typedef pair<ull, ull> pullull;
typedef pair<ll,int> plli;
typedef pair<double,int> pdi;
typedef pair<long double, int> pdbi;
typedef pair<int,pii> pipii;
typedef pair<ll,pll> plpll;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<pii> vpii;
typedef vector<vector<int>> mat;

#define rep(i,n) for (int i=0;i<(n);i++)
#define rep2(i,a,b) for (int i=(a);i<(b);i++)
#define rrep(i,n) for (int i=(n);i>0;i--)
#define rrep2(i,a,b) for (int i=(a);i>b;i--)
#define pb push_back
#define fi first
#define se second
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()

const ll hmod1 = 999999937;
const ll hmod2 = 1000000000 + 9;
const int INF = 1<<30;
const ll INFLL = 1LL<<62;
const long double EPS = 1e-12;
const ll mod = 1000000000 + 7;
//const ll mod = 998244353;
const int dx4[4] = {1, 0, -1, 0};
const int dy4[4] = {0, 1, 0, -1};
const int dx8[8] = {1, 1, 1, 0, 0, -1, -1, -1};
const int dy8[8] = {0, 1, -1, 1, -1, 0, 1, -1};
const long double pi = 3.141592653589793;

#define addm(X, Y) (X) = ((X) + ((Y) % mod) + mod) % mod
#define inside(y, x, h, w) (0 <= (y) && (y) < (h) && 0 <= (x) && (x) < (w)) ? true : false

//debug
#define DEBUG

#define DUMPOUT cerr

#ifdef DEBUG
#define dump(...) DUMPOUT<<#__VA_ARGS__<<" :["<<__FUNCTION__<<":"<<__LINE__<<"]"<<endl; DUMPOUT<<"    "; dump_func(__VA_ARGS__)
#else
#define dump(...)
#endif

void dump_func() {DUMPOUT << endl;};

template <class Head, class... Tail> void dump_func(Head&& head, Tail&&... tail) {
    DUMPOUT << head;
    if (sizeof...(Tail) == 0) DUMPOUT << " ";
    else DUMPOUT << ", ";
    dump_func(std::move(tail)...);
}

//ostream
template<typename T> ostream& operator << (ostream& os, vector<T>& vec) {
    os << "["; for (int i = 0; i<vec.size(); i++) os << vec[i] << (i + 1 == vec.size() ? "" : ", "); os << "]";
    return os;
}

template<typename T, typename U> ostream& operator << (ostream& os, pair<T, U>& pair_var) {
    os << "(" << pair_var.first << ", " << pair_var.second << ")";
    return os;
}

template<typename T, typename U> ostream& operator << (ostream& os, map<T, U>& map_var) {
    os << "[";
    for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
        os << "(" << itr->first << ", " << itr->second << ")"; itr++;  if(itr != map_var.end()) os << ", "; itr--;
    }
    os << "]";
    return os;
}

template<typename T> ostream& operator << (ostream& os, set<T>& set_var) {
    os << "[";
    for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
        os << *itr; ++itr; if(itr != set_var.end()) os << ", "; itr--;
    }
    os << "]";
    return os;
}

int n, u, v, m;

int c1[500][500], c2[500][500];
int cnty1[500], cntx1[500], cnty2[500], cntx2[500];
map<int, int> yy1, x1, y2, x2;
int Usagi, Neko;
int ex1, ex2, ex3, ex4;

signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cin >> n >> u >> v >> m;
  rep(i, n)rep(j, n) {
    cin >> c1[i][j];
    yy1[c1[i][j]] = i;
    x1[c1[i][j]] = j;
  }
  rep(i, n)rep(j, n) {
    cin >> c2[i][j];
    y2[c2[i][j]] = i;
    x2[c2[i][j]] = j;
  }
  rep(i, m) {
    int num;
    cin >> num;
    if (yy1.find(num) != yy1.end()) {
      cnty1[yy1[num]]++;
      cntx1[x1[num]]++;
      if (n == 1) {
        Usagi++;
      }
      else {
        if (yy1[num] == x1[num]) {
          ex1++;
          Usagi += (ex1 == n ? 1 : 0);
        }
        if (yy1[num] + x1[num] ==  n-1) {
          ex2++;
          Usagi += (ex2 == n ? 1 : 0);
        }
        Usagi += (cnty1[yy1[num]] == n ? 1 : 0);
        Usagi += (cntx1[x1[num]] == n ? 1 : 0);
      }
    }
    if (y2.find(num) != y2.end()) {
      cnty2[y2[num]]++;
      cntx2[x2[num]]++;
      if (n == 1) {
        Neko++;
      }
      else {
        if (y2[num] == x2[num]) {
          ex3++;
          Neko += (ex3 == n ? 1 : 0);
        }
        if (y2[num] + x2[num] ==  n-1) {
          ex4++;
          Neko += (ex4 == n ? 1 : 0);
        }
        Neko += (cnty2[y2[num]] == n ? 1 : 0);
        Neko += (cntx2[x2[num]] == n ? 1 : 0);
      }
    }
    if (Usagi >= u && Neko >= v) {
      cout << "DRAW" << endl;
      return 0;
    }
    if (Usagi >= u) {
      cout << "USAGI" << endl;
      return 0;
    }
    if (Neko >= v) {
      cout << "NEKO" << endl;
      return 0;
    }
  }
  cout << "DRAW" << endl;
}


### Prompt

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

Rabbits and cats are competing. The rules are as follows.

First, each of the two animals wrote n2 integers on a piece of paper in a square with n rows and n columns, and drew one card at a time. Shuffle two cards and draw them one by one alternately. Each time a card is drawn, the two will mark it if the same number as the card is written on their paper. The winning condition is that the number of "a set of n numbers with a mark and is in a straight line" is equal to or greater than the number of playing cards drawn at the beginning.

Answer which of the rabbit and the cat wins up to the mth card given. However, the victory or defeat is when only one of the two cards meets the victory condition when a certain card is drawn and marked. In other cases, it is a draw. Cards may be drawn even after one of them meets the victory conditions, but this does not affect the victory or defeat.



Input

Line 1: “nuvm” (square size, number of rabbit playing cards, number of cat playing cards, number of cards drawn) 2- (N + 1) Line: n2 numbers that the rabbit writes on paper ( N + 2)-(2N + 1) Line: n2 numbers that the cat writes on paper (2N + 2)-(2N + M + 1) Line: m cards drawn
1 ≤ n ≤ 500
1 ≤ u, v ≤ 13
1 ≤ m ≤ 100 000
1 ≤ (number written) ≤ 1 000 000


The number of n2 rabbits write on paper, the number of n2 cats write on paper, and the number of m cards drawn are different.

Output

Output "USAGI" if the rabbit wins, "NEKO" if the cat wins, and "DRAW" if the tie, each in one line.

Examples

Input

3 2 2 10
1 2 3
4 5 6
7 8 9
1 2 3
6 5 4
7 8 9
11
4
7
5
10
9
2
1
3
8


Output

USAGI


Input

3 2 1 10
1 2 3
4 5 6
7 8 9
1 2 3
6 5 4
7 8 9
11
4
7
5
10
9
2
1
3
8


Output

DRAW

### Response

```cpp
//#include <bits/stdc++.h>

#include <iostream>
#include <algorithm>

#include <bitset>
#include <vector>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <stack>
#include <queue>
#include <deque>
#include <cstring>
#include <string>
#include <utility>
#include <array>
#include <complex>
#include <valarray>

#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
#include <chrono>
#include <random>
#include <numeric>

#include<memory>


using namespace std;
#define int long long

typedef long long ll;
typedef unsigned long long ull;
//typedef unsigned __int128 HASH;
typedef pair<int,int> pii;
typedef pair<ll, ll> pll;
typedef pair<ull, ull> pullull;
typedef pair<ll,int> plli;
typedef pair<double,int> pdi;
typedef pair<long double, int> pdbi;
typedef pair<int,pii> pipii;
typedef pair<ll,pll> plpll;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<pii> vpii;
typedef vector<vector<int>> mat;

#define rep(i,n) for (int i=0;i<(n);i++)
#define rep2(i,a,b) for (int i=(a);i<(b);i++)
#define rrep(i,n) for (int i=(n);i>0;i--)
#define rrep2(i,a,b) for (int i=(a);i>b;i--)
#define pb push_back
#define fi first
#define se second
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()

const ll hmod1 = 999999937;
const ll hmod2 = 1000000000 + 9;
const int INF = 1<<30;
const ll INFLL = 1LL<<62;
const long double EPS = 1e-12;
const ll mod = 1000000000 + 7;
//const ll mod = 998244353;
const int dx4[4] = {1, 0, -1, 0};
const int dy4[4] = {0, 1, 0, -1};
const int dx8[8] = {1, 1, 1, 0, 0, -1, -1, -1};
const int dy8[8] = {0, 1, -1, 1, -1, 0, 1, -1};
const long double pi = 3.141592653589793;

#define addm(X, Y) (X) = ((X) + ((Y) % mod) + mod) % mod
#define inside(y, x, h, w) (0 <= (y) && (y) < (h) && 0 <= (x) && (x) < (w)) ? true : false

//debug
#define DEBUG

#define DUMPOUT cerr

#ifdef DEBUG
#define dump(...) DUMPOUT<<#__VA_ARGS__<<" :["<<__FUNCTION__<<":"<<__LINE__<<"]"<<endl; DUMPOUT<<"    "; dump_func(__VA_ARGS__)
#else
#define dump(...)
#endif

void dump_func() {DUMPOUT << endl;};

template <class Head, class... Tail> void dump_func(Head&& head, Tail&&... tail) {
    DUMPOUT << head;
    if (sizeof...(Tail) == 0) DUMPOUT << " ";
    else DUMPOUT << ", ";
    dump_func(std::move(tail)...);
}

//ostream
template<typename T> ostream& operator << (ostream& os, vector<T>& vec) {
    os << "["; for (int i = 0; i<vec.size(); i++) os << vec[i] << (i + 1 == vec.size() ? "" : ", "); os << "]";
    return os;
}

template<typename T, typename U> ostream& operator << (ostream& os, pair<T, U>& pair_var) {
    os << "(" << pair_var.first << ", " << pair_var.second << ")";
    return os;
}

template<typename T, typename U> ostream& operator << (ostream& os, map<T, U>& map_var) {
    os << "[";
    for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
        os << "(" << itr->first << ", " << itr->second << ")"; itr++;  if(itr != map_var.end()) os << ", "; itr--;
    }
    os << "]";
    return os;
}

template<typename T> ostream& operator << (ostream& os, set<T>& set_var) {
    os << "[";
    for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
        os << *itr; ++itr; if(itr != set_var.end()) os << ", "; itr--;
    }
    os << "]";
    return os;
}

int n, u, v, m;

int c1[500][500], c2[500][500];
int cnty1[500], cntx1[500], cnty2[500], cntx2[500];
map<int, int> yy1, x1, y2, x2;
int Usagi, Neko;
int ex1, ex2, ex3, ex4;

signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cin >> n >> u >> v >> m;
  rep(i, n)rep(j, n) {
    cin >> c1[i][j];
    yy1[c1[i][j]] = i;
    x1[c1[i][j]] = j;
  }
  rep(i, n)rep(j, n) {
    cin >> c2[i][j];
    y2[c2[i][j]] = i;
    x2[c2[i][j]] = j;
  }
  rep(i, m) {
    int num;
    cin >> num;
    if (yy1.find(num) != yy1.end()) {
      cnty1[yy1[num]]++;
      cntx1[x1[num]]++;
      if (n == 1) {
        Usagi++;
      }
      else {
        if (yy1[num] == x1[num]) {
          ex1++;
          Usagi += (ex1 == n ? 1 : 0);
        }
        if (yy1[num] + x1[num] ==  n-1) {
          ex2++;
          Usagi += (ex2 == n ? 1 : 0);
        }
        Usagi += (cnty1[yy1[num]] == n ? 1 : 0);
        Usagi += (cntx1[x1[num]] == n ? 1 : 0);
      }
    }
    if (y2.find(num) != y2.end()) {
      cnty2[y2[num]]++;
      cntx2[x2[num]]++;
      if (n == 1) {
        Neko++;
      }
      else {
        if (y2[num] == x2[num]) {
          ex3++;
          Neko += (ex3 == n ? 1 : 0);
        }
        if (y2[num] + x2[num] ==  n-1) {
          ex4++;
          Neko += (ex4 == n ? 1 : 0);
        }
        Neko += (cnty2[y2[num]] == n ? 1 : 0);
        Neko += (cntx2[x2[num]] == n ? 1 : 0);
      }
    }
    if (Usagi >= u && Neko >= v) {
      cout << "DRAW" << endl;
      return 0;
    }
    if (Usagi >= u) {
      cout << "USAGI" << endl;
      return 0;
    }
    if (Neko >= v) {
      cout << "NEKO" << endl;
      return 0;
    }
  }
  cout << "DRAW" << endl;
}


```