#include <bits/stdc++.h>
using namespace std;
struct coord {
  int x, y, z;
  coord() : x(0), y(0), z(0) {}
  coord(int x, int y, int z) : x(x), y(y), z(z) {}
};
coord getVector(coord p, coord p1) {
  return coord(p1.x - p.x, p1.y - p.y, p1.z - p.z);
}
long long sProduct(coord v1, coord v2) {
  return (v1.x * (long long)v2.x) + (v1.y * (long long)v2.y) +
         (v1.z * (long long)v2.z);
}
long long squareLength(coord v1) { return sProduct(v1, v1); }
bool sameLength(coord v1, coord v2) {
  return (squareLength(v1) - squareLength(v2)) == 0;
}
bool ortho(coord v1, coord v2) { return sProduct(v1, v2) == 0; }
bool isCorner(coord p, coord p1, coord p2, coord p3) {
  coord e1 = getVector(p, p1);
  coord e2 = getVector(p, p2);
  coord e3 = getVector(p, p3);
  return ortho(e1, e2) && ortho(e1, e3) && ortho(e2, e3);
}
const int cLines = 8;
const int cDimension = 3;
coord* isCube(int** input, coord* coords, int line) {
  coord* output;
  if (line < cLines) {
    coords[line] = coord(input[line][0], input[line][1], input[line][2]);
    if ((output = isCube(input, coords, line + 1)) != NULL) return output;
    coords[line] = coord(input[line][0], input[line][2], input[line][1]);
    if ((output = isCube(input, coords, line + 1)) != NULL) return output;
    coords[line] = coord(input[line][1], input[line][0], input[line][2]);
    if ((output = isCube(input, coords, line + 1)) != NULL) return output;
    coords[line] = coord(input[line][1], input[line][2], input[line][0]);
    if ((output = isCube(input, coords, line + 1)) != NULL) return output;
    coords[line] = coord(input[line][2], input[line][1], input[line][0]);
    if ((output = isCube(input, coords, line + 1)) != NULL) return output;
    coords[line] = coord(input[line][2], input[line][0], input[line][1]);
    if ((output = isCube(input, coords, line + 1)) != NULL) return output;
    return NULL;
  } else {
    long long tSize = 0;
    long long sqrLen;
    for (int i = 1; i < cLines; i++) {
      sqrLen = squareLength(getVector(coords[0], coords[i]));
      if (sqrLen > tSize) tSize = sqrLen;
    }
    if (tSize % cDimension != 0) {
      return NULL;
    }
    tSize /= cDimension;
    int counts[cDimension + 1];
    int goals[cDimension + 1] = {1, 3, 3, 1};
    int r;
    for (int i = 0; i < cLines; i++) {
      for (int d = 0; d <= cDimension; d++) counts[d] = 0;
      for (int j = 0; j < cLines; j++) {
        sqrLen = squareLength(getVector(coords[i], coords[j]));
        if (tSize != 0 && sqrLen % tSize != 0) {
          return NULL;
        }
        if (tSize == 0 && sqrLen != 0) {
          return NULL;
        }
        r = (tSize == 0 ? 0 : sqrLen / tSize);
        if (r <= cDimension) {
          counts[r]++;
          if (counts[r] > goals[r]) return NULL;
        } else {
          return NULL;
        }
      }
    }
    return coords;
  }
}
coord* isCube(int** input) {
  coord* coords = new coord[cLines];
  coords[0] = coord(input[0][0], input[0][1], input[0][2]);
  return isCube(input, coords, 1);
}
int main() {
  int** input = new int*[cLines];
  for (int l = 0; l < cLines; l++) {
    input[l] = new int[cDimension];
    for (int d = 0; d < cDimension; d++) cin >> input[l][d];
  }
  coord* output = isCube(input);
  if (output) {
    cout << "YES" << endl;
    for (int l = 0; l < cLines; l++) {
      cout << output[l].x << " " << output[l].y << " " << output[l].z << endl;
    }
  } else {
    cout << "NO" << endl;
  }
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

Peter had a cube with non-zero length of a side. He put the cube into three-dimensional space in such a way that its vertices lay at integer points (it is possible that the cube's sides are not parallel to the coordinate axes). Then he took a piece of paper and wrote down eight lines, each containing three integers — coordinates of cube's vertex (a single line contains coordinates of a single vertex, each vertex is written exactly once), put the paper on the table and left. While Peter was away, his little brother Nick decided to play with the numbers on the paper. In one operation Nick could swap some numbers inside a single line (Nick didn't swap numbers from distinct lines). Nick could have performed any number of such operations.

When Peter returned and found out about Nick's mischief, he started recollecting the original coordinates. Help Peter restore the original position of the points or else state that this is impossible and the numbers were initially recorded incorrectly.

Input

Each of the eight lines contains three space-separated integers — the numbers written on the piece of paper after Nick's mischief. All numbers do not exceed 106 in their absolute value.

Output

If there is a way to restore the cube, then print in the first line "YES". In each of the next eight lines print three integers — the restored coordinates of the points. The numbers in the i-th output line must be a permutation of the numbers in i-th input line. The numbers should represent the vertices of a cube with non-zero length of a side. If there are multiple possible ways, print any of them.

If there is no valid way, print "NO" (without the quotes) in the first line. Do not print anything else.

Examples

Input

0 0 0
0 0 1
0 0 1
0 0 1
0 1 1
0 1 1
0 1 1
1 1 1


Output

YES
0 0 0
0 0 1
0 1 0
1 0 0
0 1 1
1 0 1
1 1 0
1 1 1


Input

0 0 0
0 0 0
0 0 0
0 0 0
1 1 1
1 1 1
1 1 1
1 1 1


Output

NO

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
struct coord {
  int x, y, z;
  coord() : x(0), y(0), z(0) {}
  coord(int x, int y, int z) : x(x), y(y), z(z) {}
};
coord getVector(coord p, coord p1) {
  return coord(p1.x - p.x, p1.y - p.y, p1.z - p.z);
}
long long sProduct(coord v1, coord v2) {
  return (v1.x * (long long)v2.x) + (v1.y * (long long)v2.y) +
         (v1.z * (long long)v2.z);
}
long long squareLength(coord v1) { return sProduct(v1, v1); }
bool sameLength(coord v1, coord v2) {
  return (squareLength(v1) - squareLength(v2)) == 0;
}
bool ortho(coord v1, coord v2) { return sProduct(v1, v2) == 0; }
bool isCorner(coord p, coord p1, coord p2, coord p3) {
  coord e1 = getVector(p, p1);
  coord e2 = getVector(p, p2);
  coord e3 = getVector(p, p3);
  return ortho(e1, e2) && ortho(e1, e3) && ortho(e2, e3);
}
const int cLines = 8;
const int cDimension = 3;
coord* isCube(int** input, coord* coords, int line) {
  coord* output;
  if (line < cLines) {
    coords[line] = coord(input[line][0], input[line][1], input[line][2]);
    if ((output = isCube(input, coords, line + 1)) != NULL) return output;
    coords[line] = coord(input[line][0], input[line][2], input[line][1]);
    if ((output = isCube(input, coords, line + 1)) != NULL) return output;
    coords[line] = coord(input[line][1], input[line][0], input[line][2]);
    if ((output = isCube(input, coords, line + 1)) != NULL) return output;
    coords[line] = coord(input[line][1], input[line][2], input[line][0]);
    if ((output = isCube(input, coords, line + 1)) != NULL) return output;
    coords[line] = coord(input[line][2], input[line][1], input[line][0]);
    if ((output = isCube(input, coords, line + 1)) != NULL) return output;
    coords[line] = coord(input[line][2], input[line][0], input[line][1]);
    if ((output = isCube(input, coords, line + 1)) != NULL) return output;
    return NULL;
  } else {
    long long tSize = 0;
    long long sqrLen;
    for (int i = 1; i < cLines; i++) {
      sqrLen = squareLength(getVector(coords[0], coords[i]));
      if (sqrLen > tSize) tSize = sqrLen;
    }
    if (tSize % cDimension != 0) {
      return NULL;
    }
    tSize /= cDimension;
    int counts[cDimension + 1];
    int goals[cDimension + 1] = {1, 3, 3, 1};
    int r;
    for (int i = 0; i < cLines; i++) {
      for (int d = 0; d <= cDimension; d++) counts[d] = 0;
      for (int j = 0; j < cLines; j++) {
        sqrLen = squareLength(getVector(coords[i], coords[j]));
        if (tSize != 0 && sqrLen % tSize != 0) {
          return NULL;
        }
        if (tSize == 0 && sqrLen != 0) {
          return NULL;
        }
        r = (tSize == 0 ? 0 : sqrLen / tSize);
        if (r <= cDimension) {
          counts[r]++;
          if (counts[r] > goals[r]) return NULL;
        } else {
          return NULL;
        }
      }
    }
    return coords;
  }
}
coord* isCube(int** input) {
  coord* coords = new coord[cLines];
  coords[0] = coord(input[0][0], input[0][1], input[0][2]);
  return isCube(input, coords, 1);
}
int main() {
  int** input = new int*[cLines];
  for (int l = 0; l < cLines; l++) {
    input[l] = new int[cDimension];
    for (int d = 0; d < cDimension; d++) cin >> input[l][d];
  }
  coord* output = isCube(input);
  if (output) {
    cout << "YES" << endl;
    for (int l = 0; l < cLines; l++) {
      cout << output[l].x << " " << output[l].y << " " << output[l].z << endl;
    }
  } else {
    cout << "NO" << endl;
  }
  return 0;
}

```