#include <bits/stdc++.h>
using namespace std;
long long readi() {
  long long input = 0;
  char c = ' ';
  while (c < '-') {
    c = getchar();
  }
  bool negative = false;
  if (c == '-') {
    negative = true;
    c = getchar();
  }
  while (c >= '0') {
    input = 10 * input + (c - '0');
    c = getchar();
  }
  if (negative) {
    input = -input;
  }
  return input;
}
void printi(long long output) {
  if (output == 0) {
    putchar('0');
    return;
  }
  if (output < 0) {
    putchar('-');
    output = -output;
  }
  int aout[20];
  int ilen = 0;
  while (output) {
    aout[ilen] = ((output % 10));
    output /= 10;
    ilen++;
  }
  for (int i = ilen - 1; i >= 0; i--) {
    putchar(aout[i] + '0');
  }
  return;
}
string reads() {
  string input = "";
  char c = ' ';
  while (c <= ' ') {
    c = getchar();
  }
  while (c > ' ') {
    input += c;
    c = getchar();
  }
  return input;
}
void prints(string output) {
  for (int i = 0; i < output.length(); i++) {
    putchar(output[i]);
  }
  return;
}
long long getrand() {
  long long rand1 = (rand() % 536870912);
  long long rand2 = (rand() % 536870912);
  return (rand1 * 536870912ll + rand2);
}
int N;
long long arr[5][1010];
bool bad[1010];
int ans;
long long scalar(long long a, long long b, long long c) {
  long long res = 0ll;
  for (long long i = 0; i < 5; i++) {
    res += ((arr[i][b] - arr[i][a]) * (arr[i][c] - arr[i][a]));
  }
  return res;
}
int32_t main() {
  srand(time(NULL));
  cout << fixed << setprecision(10);
  cerr << fixed << setprecision(10);
  ios_base::sync_with_stdio(false);
  if (fopen("cf850a.in", "r")) {
    freopen("cf850a.in", "r", stdin);
  }
  cin >> N;
  for (int i = 0; i < N; i++) {
    for (int j = 0; j < 5; j++) {
      cin >> arr[j][i];
    }
  }
  if (N >= 100) {
    cout << "0\n";
    return 0;
  }
  for (int i = 0; i < N; i++) {
    for (int j = 0; j < N; j++) {
      if (j == i) {
        continue;
      }
      for (int k = j + 1; k < N; k++) {
        if (k == i) {
          continue;
        }
        if (scalar(i, j, k) > 0) {
          bad[i] = true;
        }
      }
    }
  }
  for (int i = 0; i < N; i++) {
    if (!bad[i]) {
      ans++;
    }
  }
  cout << ans << '\n';
  for (int i = 0; i < N; i++) {
    if (!bad[i]) {
      cout << i + 1 << '\n';
    }
  }
  return 0;
}

### Prompt

Generate 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>
using namespace std;
long long readi() {
  long long input = 0;
  char c = ' ';
  while (c < '-') {
    c = getchar();
  }
  bool negative = false;
  if (c == '-') {
    negative = true;
    c = getchar();
  }
  while (c >= '0') {
    input = 10 * input + (c - '0');
    c = getchar();
  }
  if (negative) {
    input = -input;
  }
  return input;
}
void printi(long long output) {
  if (output == 0) {
    putchar('0');
    return;
  }
  if (output < 0) {
    putchar('-');
    output = -output;
  }
  int aout[20];
  int ilen = 0;
  while (output) {
    aout[ilen] = ((output % 10));
    output /= 10;
    ilen++;
  }
  for (int i = ilen - 1; i >= 0; i--) {
    putchar(aout[i] + '0');
  }
  return;
}
string reads() {
  string input = "";
  char c = ' ';
  while (c <= ' ') {
    c = getchar();
  }
  while (c > ' ') {
    input += c;
    c = getchar();
  }
  return input;
}
void prints(string output) {
  for (int i = 0; i < output.length(); i++) {
    putchar(output[i]);
  }
  return;
}
long long getrand() {
  long long rand1 = (rand() % 536870912);
  long long rand2 = (rand() % 536870912);
  return (rand1 * 536870912ll + rand2);
}
int N;
long long arr[5][1010];
bool bad[1010];
int ans;
long long scalar(long long a, long long b, long long c) {
  long long res = 0ll;
  for (long long i = 0; i < 5; i++) {
    res += ((arr[i][b] - arr[i][a]) * (arr[i][c] - arr[i][a]));
  }
  return res;
}
int32_t main() {
  srand(time(NULL));
  cout << fixed << setprecision(10);
  cerr << fixed << setprecision(10);
  ios_base::sync_with_stdio(false);
  if (fopen("cf850a.in", "r")) {
    freopen("cf850a.in", "r", stdin);
  }
  cin >> N;
  for (int i = 0; i < N; i++) {
    for (int j = 0; j < 5; j++) {
      cin >> arr[j][i];
    }
  }
  if (N >= 100) {
    cout << "0\n";
    return 0;
  }
  for (int i = 0; i < N; i++) {
    for (int j = 0; j < N; j++) {
      if (j == i) {
        continue;
      }
      for (int k = j + 1; k < N; k++) {
        if (k == i) {
          continue;
        }
        if (scalar(i, j, k) > 0) {
          bad[i] = true;
        }
      }
    }
  }
  for (int i = 0; i < N; i++) {
    if (!bad[i]) {
      ans++;
    }
  }
  cout << ans << '\n';
  for (int i = 0; i < N; i++) {
    if (!bad[i]) {
      cout << i + 1 << '\n';
    }
  }
  return 0;
}

```