#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:1024000000,1024000000")
using namespace std;
const int INF = 0x3f3f3f3f;
const long long LINF = 0x3f3f3f3f3f3f3f3fLL;
const int dx[] = {-1, 0, 1, 0, 1, -1, -1, 1};
const int dy[] = {0, 1, 0, -1, -1, 1, -1, 1};
const int maxn = 1e3 + 10;
const int maxx = 1e6 + 100;
const double EPS = 1e-8;
const double eps = 1e-8;
const int mod = 1e9 + 7;
template <class T>
inline T min(T a, T b, T c) {
  return min(min(a, b), c);
}
template <class T>
inline T max(T a, T b, T c) {
  return max(max(a, b), c);
}
template <class T>
inline T min(T a, T b, T c, T d) {
  return min(min(a, b), min(c, d));
}
template <class T>
inline T max(T a, T b, T c, T d) {
  return max(max(a, b), max(c, d));
}
template <class T>
inline bool scan_d(T &ret) {
  char c;
  int sgn;
  if (c = getchar(), c == EOF) {
    return 0;
  }
  while (c != '-' && (c < '0' || c > '9')) {
    c = getchar();
  }
  sgn = (c == '-') ? -1 : 1;
  ret = (c == '-') ? 0 : (c - '0');
  while (c = getchar(), c >= '0' && c <= '9') {
    ret = ret * 10 + (c - '0');
  }
  ret *= sgn;
  return 1;
}
inline bool scan_lf(double &num) {
  char in;
  double Dec = 0.1;
  bool IsN = false, IsD = false;
  in = getchar();
  if (in == EOF) return false;
  while (in != '-' && in != '.' && (in < '0' || in > '9')) in = getchar();
  if (in == '-') {
    IsN = true;
    num = 0;
  } else if (in == '.') {
    IsD = true;
    num = 0;
  } else
    num = in - '0';
  if (!IsD) {
    while (in = getchar(), in >= '0' && in <= '9') {
      num *= 10;
      num += in - '0';
    }
  }
  if (in != '.') {
    if (IsN) num = -num;
    return true;
  } else {
    while (in = getchar(), in >= '0' && in <= '9') {
      num += Dec * (in - '0');
      Dec *= 0.1;
    }
  }
  if (IsN) num = -num;
  return true;
}
void Out(long long a) {
  if (a < 0) {
    putchar('-');
    a = -a;
  }
  if (a >= 10) Out(a / 10);
  putchar(a % 10 + '0');
}
void print(long long a) { Out(a), puts(""); }
int n;
int vis[maxn];
struct node {
  double a, b, c, d, e;
} Q[maxn];
double Dot(node A, node B) {
  return A.a * B.a + A.b * B.b + A.c * B.c + A.d * B.d + A.e * B.e;
}
double Length(node A) { return sqrt(Dot(A, A)); }
double Angle(node A, node B) { return acos(Dot(A, B) / Length(A) / Length(B)); }
node vv(node A, node B) {
  node v1;
  v1.a = A.a - B.a;
  v1.b = A.b - B.b;
  v1.c = A.c - B.c;
  v1.d = A.d - B.d;
  v1.e = A.e - B.e;
  return v1;
}
int main() {
  scan_d(n);
  for (int i = 1; i <= n; i++) {
    scanf("%lf%lf%lf%lf%lf", &Q[i].a, &Q[i].b, &Q[i].c, &Q[i].d, &Q[i].e);
  }
  if (n > 243) {
    puts("0");
    return 0;
  }
  node v1, v2;
  int cnt = 0;
  for (int i = 1; i <= n; i++) {
    int flag = 0;
    for (int j = 1; j <= n; j++) {
      if (i == j) continue;
      for (int k = 1; k <= n; k++) {
        if (j == k || k == i) continue;
        v1 = vv(Q[i], Q[j]);
        v2 = vv(Q[i], Q[k]);
        double ang = Angle(v1, v2);
        if (ang < acos(-1) / 2.0 - eps) {
          flag = 1;
          break;
        }
      }
      if (flag) break;
    }
    if (!flag) {
      vis[cnt++] = i;
    }
  }
  print(cnt);
  for (int i = 0; i < cnt; i++) print(vis[i]);
}

### Prompt

Your task is to create a cpp solution to the following problem:

You are given set of n points in 5-dimensional space. The points are labeled from 1 to n. No two points coincide.

We will call point a bad if there are different points b and c, not equal to a, from the given set such that angle between vectors <image> and <image> is acute (i.e. strictly less than <image>). Otherwise, the point is called good.

The angle between vectors <image> and <image> in 5-dimensional space is defined as <image>, where <image> is the scalar product and <image> is length of <image>.

Given the list of points, print the indices of the good points in ascending order.

Input

The first line of input contains a single integer n (1 ≤ n ≤ 103) — the number of points.

The next n lines of input contain five integers ai, bi, ci, di, ei (|ai|, |bi|, |ci|, |di|, |ei| ≤ 103) — the coordinates of the i-th point. All points are distinct.

Output

First, print a single integer k — the number of good points.

Then, print k integers, each on their own line — the indices of the good points in ascending order.

Examples

Input

6
0 0 0 0 0
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1


Output

1
1


Input

3
0 0 1 2 0
0 0 9 2 0
0 0 5 9 0


Output

0

Note

In the first sample, the first point forms exactly a <image> angle with all other pairs of points, so it is good.

In the second sample, along the cd plane, we can see the points look as follows:

<image>

We can see that all angles here are acute, so no points are good.

### Response

```cpp
#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:1024000000,1024000000")
using namespace std;
const int INF = 0x3f3f3f3f;
const long long LINF = 0x3f3f3f3f3f3f3f3fLL;
const int dx[] = {-1, 0, 1, 0, 1, -1, -1, 1};
const int dy[] = {0, 1, 0, -1, -1, 1, -1, 1};
const int maxn = 1e3 + 10;
const int maxx = 1e6 + 100;
const double EPS = 1e-8;
const double eps = 1e-8;
const int mod = 1e9 + 7;
template <class T>
inline T min(T a, T b, T c) {
  return min(min(a, b), c);
}
template <class T>
inline T max(T a, T b, T c) {
  return max(max(a, b), c);
}
template <class T>
inline T min(T a, T b, T c, T d) {
  return min(min(a, b), min(c, d));
}
template <class T>
inline T max(T a, T b, T c, T d) {
  return max(max(a, b), max(c, d));
}
template <class T>
inline bool scan_d(T &ret) {
  char c;
  int sgn;
  if (c = getchar(), c == EOF) {
    return 0;
  }
  while (c != '-' && (c < '0' || c > '9')) {
    c = getchar();
  }
  sgn = (c == '-') ? -1 : 1;
  ret = (c == '-') ? 0 : (c - '0');
  while (c = getchar(), c >= '0' && c <= '9') {
    ret = ret * 10 + (c - '0');
  }
  ret *= sgn;
  return 1;
}
inline bool scan_lf(double &num) {
  char in;
  double Dec = 0.1;
  bool IsN = false, IsD = false;
  in = getchar();
  if (in == EOF) return false;
  while (in != '-' && in != '.' && (in < '0' || in > '9')) in = getchar();
  if (in == '-') {
    IsN = true;
    num = 0;
  } else if (in == '.') {
    IsD = true;
    num = 0;
  } else
    num = in - '0';
  if (!IsD) {
    while (in = getchar(), in >= '0' && in <= '9') {
      num *= 10;
      num += in - '0';
    }
  }
  if (in != '.') {
    if (IsN) num = -num;
    return true;
  } else {
    while (in = getchar(), in >= '0' && in <= '9') {
      num += Dec * (in - '0');
      Dec *= 0.1;
    }
  }
  if (IsN) num = -num;
  return true;
}
void Out(long long a) {
  if (a < 0) {
    putchar('-');
    a = -a;
  }
  if (a >= 10) Out(a / 10);
  putchar(a % 10 + '0');
}
void print(long long a) { Out(a), puts(""); }
int n;
int vis[maxn];
struct node {
  double a, b, c, d, e;
} Q[maxn];
double Dot(node A, node B) {
  return A.a * B.a + A.b * B.b + A.c * B.c + A.d * B.d + A.e * B.e;
}
double Length(node A) { return sqrt(Dot(A, A)); }
double Angle(node A, node B) { return acos(Dot(A, B) / Length(A) / Length(B)); }
node vv(node A, node B) {
  node v1;
  v1.a = A.a - B.a;
  v1.b = A.b - B.b;
  v1.c = A.c - B.c;
  v1.d = A.d - B.d;
  v1.e = A.e - B.e;
  return v1;
}
int main() {
  scan_d(n);
  for (int i = 1; i <= n; i++) {
    scanf("%lf%lf%lf%lf%lf", &Q[i].a, &Q[i].b, &Q[i].c, &Q[i].d, &Q[i].e);
  }
  if (n > 243) {
    puts("0");
    return 0;
  }
  node v1, v2;
  int cnt = 0;
  for (int i = 1; i <= n; i++) {
    int flag = 0;
    for (int j = 1; j <= n; j++) {
      if (i == j) continue;
      for (int k = 1; k <= n; k++) {
        if (j == k || k == i) continue;
        v1 = vv(Q[i], Q[j]);
        v2 = vv(Q[i], Q[k]);
        double ang = Angle(v1, v2);
        if (ang < acos(-1) / 2.0 - eps) {
          flag = 1;
          break;
        }
      }
      if (flag) break;
    }
    if (!flag) {
      vis[cnt++] = i;
    }
  }
  print(cnt);
  for (int i = 0; i < cnt; i++) print(vis[i]);
}

```