Problem: Little Petya very much likes rectangles and especially squares. Recently he has received 8 points on the plane as a gift from his mother. The points are pairwise distinct. Petya decided to split them into two sets each containing 4 points so that the points from the first set lay at the vertexes of some square and the points from the second set lay at the vertexes of a rectangle. Each point of initial 8 should belong to exactly one set. It is acceptable for a rectangle from the second set was also a square. If there are several partitions, Petya will be satisfied by any of them. Help him find such partition. Note that the rectangle and the square from the partition should have non-zero areas. The sides of the figures do not have to be parallel to the coordinate axes, though it might be the case.

Input

You are given 8 pairs of integers, a pair per line — the coordinates of the points Petya has. The absolute value of all coordinates does not exceed 104. It is guaranteed that no two points coincide.

Output

Print in the first output line "YES" (without the quotes), if the desired partition exists. In the second line output 4 space-separated numbers — point indexes from the input, which lie at the vertexes of the square. The points are numbered starting from 1. The numbers can be printed in any order. In the third line print the indexes of points lying at the vertexes of a rectangle in the similar format. All printed numbers should be pairwise distinct.

If the required partition does not exist, the first line should contain the word "NO" (without the quotes), after which no output is needed.

Examples

Input

0 0
10 11
10 0
0 11
1 1
2 2
2 1
1 2


Output

YES
5 6 7 8
1 2 3 4


Input

0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7


Output

NO


Input

0 0
4 4
4 0
0 4
1 2
2 3
3 2
2 1


Output

YES
1 2 3 4
5 6 7 8

Note

Pay attention to the third example: the figures do not necessarily have to be parallel to the coordinate axes.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const double PI = acos(-1.0);
template <class T>
void out(const vector<T> &a) {
  cout << "array: ";
  for (int i = 0; i < (int)a.size(); i++) cout << a[i] << " ";
  cout << endl;
  cout.flush();
}
void binprint(int mask, int n) {
  int i;
  string s = "";
  do {
    s += (mask % 2 + '0');
    mask /= 2;
  } while (mask);
  reverse(s.begin(), s.end());
  s = string((n - (int)s.size() > 0 ? n - (int)s.size() : 0), '0') + s;
  for (i = (int)s.size() - n; i < (int)s.size(); i++) printf("%c", s[i]);
  printf("\n");
}
void ASCII_Chart() {
  int i, j, k;
  printf("ASCII Chart:(30-129)\n");
  for (i = 30; i <= 50; i++) {
    for (j = 0; j < 5; j++) {
      k = i + j * 20;
      printf("%3d---> '%c'   ", k, k);
    }
    printf("\n");
  }
}
template <class T>
inline T gcd(T a, T b) {
  if (a < 0) return gcd(-a, b);
  if (b < 0) return gcd(a, -b);
  return (b == 0) ? a : gcd(b, a % b);
}
template <class T>
inline T lcm(T a, T b) {
  if (a < 0) return lcm(-a, b);
  if (b < 0) return lcm(a, -b);
  return a * (b / gcd(a, b));
}
template <class T>
T Abs(T x) {
  return x > 0 ? x : -x;
}
template <class T>
inline T sqr(T x) {
  return x * x;
}
template <class T>
inline T Mod(T n, T m) {
  return (n % m + m) % m;
}
int BigMod(long long B, long long P, long long M) {
  long long R = 1;
  while (P > 0) {
    if (P % 2 == 1) {
      R = (R * B) % M;
    }
    P /= 2;
    B = (B * B) % M;
  }
  return (int)R;
}
long long mulmod(long long a, long long b, long long c) {
  long long x = 0, y = a % c;
  while (b > 0) {
    if (b % 2 == 1) {
      x = (x + y) % c;
    }
    y = (y * 2) % c;
    b /= 2;
  }
  return x % c;
}
long long mpow(long long x, long long k) {
  if (k == 0) return 1;
  long long r = mpow(x, k / 2);
  return k % 2 ? (r * r * x) : (r * r);
}
template <class T>
inline vector<pair<T, int> > factorize(T n) {
  vector<pair<T, int> > R;
  for (T i = 2; n > 1;) {
    if (n % i == 0) {
      int C = 0;
      for (; n % i == 0; C++, n /= i)
        ;
      R.push_back(make_pair(i, C));
    }
    i++;
    if (i > n / i) i = n;
  }
  if (n > 1) R.push_back(make_pair(n, 1));
  return R;
}
vector<string> SubstringGenerate(string str) {
  int i, j, len;
  vector<string> store;
  len = (int)str.size();
  for (i = 0; i < len; i++)
    for (j = i; j <= len; j++) store.push_back(str.substr(i, j - i + 1));
  return store;
}
template <class T>
inline bool isPrime(T n) {
  if (n <= 1) return false;
  for (T i = 2; i * i <= n; i++)
    if (n % i == 0) return false;
  return true;
}
bool IsVowel(char ch) {
  ch = tolower(ch);
  if (ch == 'a' || ch == 'e' || ch == 'i' || ch == 'o' || ch == 'u')
    return true;
  return false;
}
bool isUpperCase(char c) { return c >= 'A' && c <= 'Z'; }
bool isLowerCase(char c) { return c >= 'a' && c <= 'z'; }
bool isLetter(char c) { return c >= 'A' && c <= 'Z' || c >= 'a' && c <= 'z'; }
bool isDigit(char c) { return c >= '0' && c <= '9'; }
double deg2rad(double x) { return (PI * x) / 180.0; }
double rad2deg(double x) { return (180.0 * x) / PI; }
template <class T>
string toString(T n) {
  ostringstream oss;
  oss << n;
  oss.flush();
  return oss.str();
}
int toInt(string s) {
  int r = 0;
  istringstream sin(s);
  sin >> r;
  return r;
}
long long toLl(string s) {
  long long r = 0;
  istringstream sin(s);
  sin >> r;
  return r;
}
double toDouble(string s) {
  double r = 0;
  istringstream sin(s);
  sin >> r;
  return r;
}
template <typename T>
static void splitstr(const string &s, vector<T> &out) {
  istringstream in(s);
  out.clear();
  copy(istream_iterator<T>(in), istream_iterator<T>(), back_inserter(out));
}
template <class T>
void debug(T e) {
  cout << e << endl;
}
template <class T1, class T2>
void debug(T1 e1, T2 e2) {
  cout << e1 << "\t" << e2 << endl;
}
template <class T1, class T2, class T3>
void debug(T1 e1, T2 e2, T3 e3) {
  cout << e1 << "\t" << e2 << "\t" << e3 << endl;
}
template <class T1, class T2, class T3, class T4>
void debug(T1 e1, T2 e2, T3 e3, T4 e4) {
  cout << e1 << "\t" << e2 << "\t" << e3 << "\t" << e4 << endl;
}
template <class T1, class T2, class T3, class T4, class T5>
void debug(T1 e1, T2 e2, T3 e3, T4 e4, T5 e5) {
  cout << e1 << "\t" << e2 << "\t" << e3 << "\t" << e4 << "\t" << e5 << endl;
}
template <class T>
void debug(vector<T> e) {
  int i;
  for (i = 0; i < (int)e.size(); i++) cout << e[i] << " ";
  cout << endl;
}
template <class T>
void debug(vector<T> e, int n) {
  int i;
  for (i = 0; i < n; i++) cout << e[i] << " ";
  cout << endl;
}
template <class T>
void debug(vector<basic_string<T> > e) {
  int i, j;
  for (i = 0; i < (int)e.size(); i++) {
    for (j = 0; j < (int)e[i].size(); j++) cout << e[i][j];
    cout << endl;
  }
  cout << endl;
}
template <class T>
void debug(vector<basic_string<T> > e, int row, int col) {
  int i, j;
  for (i = 0; i < row; i++) {
    for (j = 0; j < col; j++) cout << e[i][j];
    cout << endl;
  }
  cout << endl;
}
template <class T>
void debug(vector<vector<T> > e, int row, int col) {
  int i, j;
  for (i = 0; i < row; i++) {
    for (j = 0; j < col; j++) cout << e[i][j] << "\t";
    cout << endl;
  }
  cout << endl;
}
template <class T>
void debug(T e[1000000][1000000], int row, int col) {
  int i, j;
  for (i = 0; i < row; i++) {
    for (j = 0; j < col; j++) cout << e[i][j] << " ";
    cout << endl;
  }
}
template <class T>
void debug(T e[], int row) {
  int i;
  for (i = 0; i < row; i++) cout << e[i] << " ";
  cout << endl;
}
typedef struct {
  int x, y;
} P;
P pvt;
bool convex_com(P a, P b) {
  int c = ((a.x - pvt.x) * (b.y - pvt.y) - (b.x - pvt.x) * (a.y - pvt.y));
  if (c < 0)
    return false;
  else if (c == 0) {
    int r1 = ((a.x - pvt.x) * (a.x - pvt.x) + (a.y - pvt.y) * (a.y - pvt.y));
    int r2 = ((b.x - pvt.x) * (b.x - pvt.x) + (b.y - pvt.y) * (b.y - pvt.y));
    return r1 < r2;
  }
  return true;
}
bool isSquare(vector<P> v) {
  long long a = (v[0].x - v[1].x) * (v[0].x - v[1].x) +
                (v[0].y - v[1].y) * (v[0].y - v[1].y);
  long long b = (v[1].x - v[2].x) * (v[1].x - v[2].x) +
                (v[1].y - v[2].y) * (v[1].y - v[2].y);
  long long c = (v[2].x - v[3].x) * (v[2].x - v[3].x) +
                (v[2].y - v[3].y) * (v[2].y - v[3].y);
  long long d = (v[3].x - v[0].x) * (v[3].x - v[0].x) +
                (v[3].y - v[0].y) * (v[3].y - v[0].y);
  int r0 = ((v[3].x - v[0].x) * (v[1].x - v[0].x) +
            (v[3].y - v[0].y) * (v[1].y - v[0].y));
  int r1 = ((v[0].x - v[1].x) * (v[2].x - v[1].x) +
            (v[0].y - v[1].y) * (v[2].y - v[1].y));
  int r2 = ((v[1].x - v[2].x) * (v[3].x - v[2].x) +
            (v[1].y - v[2].y) * (v[3].y - v[2].y));
  int r3 = ((v[2].x - v[3].x) * (v[0].x - v[3].x) +
            (v[2].y - v[3].y) * (v[0].y - v[3].y));
  if (r0 || r1 || r2 || r3) return false;
  if (a == b && b == c && c == d) return true;
  return false;
}
bool isRectangle(vector<P> v) {
  long long a = (v[0].x - v[1].x) * (v[0].x - v[1].x) +
                (v[0].y - v[1].y) * (v[0].y - v[1].y);
  long long b = (v[1].x - v[2].x) * (v[1].x - v[2].x) +
                (v[1].y - v[2].y) * (v[1].y - v[2].y);
  long long c = (v[2].x - v[3].x) * (v[2].x - v[3].x) +
                (v[2].y - v[3].y) * (v[2].y - v[3].y);
  long long d = (v[3].x - v[0].x) * (v[3].x - v[0].x) +
                (v[3].y - v[0].y) * (v[3].y - v[0].y);
  int r0 = ((v[3].x - v[0].x) * (v[1].x - v[0].x) +
            (v[3].y - v[0].y) * (v[1].y - v[0].y));
  int r1 = ((v[0].x - v[1].x) * (v[2].x - v[1].x) +
            (v[0].y - v[1].y) * (v[2].y - v[1].y));
  int r2 = ((v[1].x - v[2].x) * (v[3].x - v[2].x) +
            (v[1].y - v[2].y) * (v[3].y - v[2].y));
  int r3 = ((v[2].x - v[3].x) * (v[0].x - v[3].x) +
            (v[2].y - v[3].y) * (v[0].y - v[3].y));
  if (r0 || r1 || r2 || r3) return false;
  if (a == c && b == d) return true;
  return false;
}
int main() {
  bool fl;
  int i, k, in;
  vector<int> r;
  vector<P> v, p1, p2;
  P temp;
  for (k = 0; k < 8; k++) {
    cin >> temp.x >> temp.y;
    v.push_back(temp);
    r.push_back(k + 1);
  }
  fl = 0;
  do {
    p1.clear();
    p1.push_back(v[r[0] - 1]);
    p1.push_back(v[r[1] - 1]);
    p1.push_back(v[r[2] - 1]);
    p1.push_back(v[r[3] - 1]);
    p2.clear();
    p2.push_back(v[r[4] - 1]);
    p2.push_back(v[r[5] - 1]);
    p2.push_back(v[r[6] - 1]);
    p2.push_back(v[r[7] - 1]);
    pvt = p1[0];
    in = 0;
    for (i = 1; i < 4; i++) {
      if (p1[i].y < pvt.y) {
        pvt = p1[i];
        in = i;
      } else if ((p1[i].y == pvt.y) && (p1[i].x < pvt.x)) {
        pvt = p1[i];
        in = i;
      }
    }
    swap(p1[0], p1[in]);
    sort((p1).begin(), (p1).end(), convex_com);
    pvt = p2[0];
    in = 0;
    for (i = 1; i < 4; i++) {
      if (p2[i].y < pvt.y) {
        pvt = p2[i];
        in = i;
      } else if ((p2[i].y == pvt.y) && (p2[i].x < pvt.x)) {
        pvt = p2[i];
        in = i;
      }
    }
    swap(p2[0], p2[in]);
    sort((p2).begin(), (p2).end(), convex_com);
    if (isSquare(p1) && isRectangle(p2)) {
      fl = 1;
      goto zaf;
    }
  } while (next_permutation(r.begin(), r.end()));
zaf:;
  if (fl) {
    cout << "YES" << endl;
    cout << r[0] << " " << r[1] << " " << r[2] << " " << r[3] << endl;
    cout << r[4] << " " << r[5] << " " << r[6] << " " << r[7] << endl;
  } else
    cout << "NO" << endl;
  return 0;
}