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class Solution {
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 public:
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  int projectionArea(vector<vector<int>> &grid) {
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    int res = 0;
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    // X-Y ( top )
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    for (int i = 0; i < grid.size(); i++) {
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      for (int j = 0; j < grid[0].size(); j++) {
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        if (grid[i][j]) // if some cubes are present it is seen as of area 1
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                        // from top
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          res++;
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      }
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    }
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    // Z-X ( front )
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    for (int i = 0; i < grid.size(); i++) {
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      int m = grid[i][0];
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      for (int j = 1; j < grid[0].size(); j++) {
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        m = max(m, grid[i][j]); // from front, the tower with heightest height
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                                // can only be seen in column
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      }
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      res += m;
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    }
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    // Z-Y ( side )
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    for (int j = 0; j < grid[0].size(); j++) {
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      int m = grid[0][j];
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      for (int i = 1; i < grid.size(); i++) {
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        m = max(m, grid[i][j]); // // from side, the tower with heightest height
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                                // can only be seen in row
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      }
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      res += m;
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    }
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    return res;
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  }
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};