class Solution {
public:
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        int m = matrix.size(), n = m? matrix[0].size(): 0;
        vector<vector<int>> padding(m + 2, vector<int>(n + 2, INT_MIN));
        vector<pair<int, int>> dirs = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
        for(int i = 0; i < m; ++i)
            for(int j = 0; j < n; ++j)
                padding[i + 1][j + 1] = matrix[i][j];
        vector<vector<int>> outdegrees(m + 2, vector<int>(n + 2, 0));
        for(int i = 1; i <= m; ++i)
        {
            for(int j = 1; j <= n; ++j)
            {
                for(auto& dir: dirs)
                {
                    if(padding[i][j] < padding[i + dir.first][j + dir.second])
                        ++outdegrees[i][j];
                }

            }
        }

        //get leaves
        queue<int> leaves;
        for(int i = 1; i <= m; ++i)
            for(int j = 1; j <= n; ++j)
                if(!outdegrees[i][j])
                    leaves.push(i * (n + 2) + j);

        //peeling onion
        int len = 0;
        while(leaves.size())
        {
            ++len;
            int size = leaves.size();
            while(size-- > 0)
            {
                int leave = leaves.front();
                leaves.pop();
                int i = leave / (n + 2), j = leave % (n + 2);
                for(auto& dir: dirs)
                {
                    if(padding[i][j] > padding[i + dir.first][j + dir.second])
                        if(--outdegrees[i + dir.first][j + dir.second] == 0)
                           leaves.push((i + dir.first) * (n + 2) + j + dir.second);
                }
            }
        }
        return len;
    }
};