vector<vector<int>> updateMatrix(vector<vector<int>>& mat) {

int n = mat.size(), m = mat[0].size();

vector<vector<int>> dis(n, vector<int>(m, INT_MAX));

// dis[i][j] = nearest distance (i, j) to nearest 0

queue<loc> q;

for(int i = 0; i < n; i++) {

for(int j = 0; j < m; j++) {

if (mat[i][j] == 0) {

q.push({i, j});

dis[i][j] = 0;

}

}

}

while(!q.empty()) {

// loc cur = q.front();

// int x = cur.first, y = cur.second;

auto [x, y] = q.front(); // current loc in mat, structured binding in C++

q.pop();

// (2,3) -> (1, 3) up, (3, 3) down, +1 -1 on the columns as well

for(int k = 0; k < 4; k++) {

int nx = x + dx[k], ny = y + dy[k];

if (0 <= nx && nx < n && 0 <= ny && ny < m) {

// valid neighbour

if (dis[nx][ny] == INT_MAX) {

dis[nx][ny] = 1 + dis[x][y];

q.push({nx, ny});

}

}

}

}

return dis;

}