#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>

using namespace std;

struct Line {
    int x1, y1, x2, y2, index;

    Line(int x1, int y1, int x2, int y2, int index) : x1(x1), y1(y1), x2(x2), y2(y2), index(index) {}
};

int orientation(int x1, int y1, int x2, int y2, int x3, int y3) {
    int val = (y2 - y1) * (x3 - x2) - (x2 - x1) * (y3 - y2);
    if (val == 0) return 0;
    return (val > 0) ? 1 : 2;
}

bool onSegment(int x1, int y1, int x2, int y2, int x3, int y3) {
    return (x2 <= max(x1, x3) && x2 >= min(x1, x3) &&
            y2 <= max(y1, y3) && y2 >= min(y1, y3));
}

bool doIntersect(Line& l1, Line& l2) {
    int o1 = orientation(l1.x1, l1.y1, l1.x2, l1.y2, l2.x1, l2.y1);
    int o2 = orientation(l1.x1, l1.y1, l1.x2, l1.y2, l2.x2, l2.y2);
    int o3 = orientation(l2.x1, l2.y1, l2.x2, l2.y2, l1.x1, l1.y1);
    int o4 = orientation(l2.x1, l2.y1, l2.x2, l2.y2, l1.x2, l1.y2);

    if (o1 != o2 && o3 != o4)
        return true;

    if (o1 == 0 && onSegment(l1.x1, l1.y1, l2.x1, l2.y1, l1.x2, l1.y2)) return true;
    if (o2 == 0 && onSegment(l1.x1, l1.y1, l2.x2, l2.y2, l1.x2, l1.y2)) return true;
    if (o3 == 0 && onSegment(l2.x1, l2.y1, l1.x1, l1.y1, l2.x2, l2.y2)) return true;
    if (o4 == 0 && onSegment(l2.x1, l2.y1, l1.x2, l1.y2, l2.x2, l2.y2)) return true;

    return false;
}

pair<int, vector<int>> findBeautifulPoint(vector<Line>& lines) {
    vector<pair<int, int>> intersections;

    for (int i = 0; i < lines.size(); i++) {
        for (int j = i + 1; j < lines.size(); j++) {
            if (doIntersect(lines[i], lines[j])) {
                int x1 = lines[i].x1, y1 = lines[i].y1;
                int x2 = lines[i].x2, y2 = lines[i].y2;
                int x3 = lines[j].x1, y3 = lines[j].y1;
                int x4 = lines[j].x2, y4 = lines[j].y2;

                int x = (x1 + x2 + x3 + x4) / 4;
                int y = (y1 + y2 + y3 + y4) / 4;

                intersections.push_back({x, y});
            }
        }
    }

    sort(intersections.begin(), intersections.end());

    int m = intersections.size();
    int minDiff = INT_MAX;
    int minPosDiff = INT_MAX;
    int bestIndex = -1;

    for (int i = 0; i < m - 1; i++) {
        int diff = abs(intersections[i + 1].first - intersections[i].first) +
                   abs(intersections[i + 1].second - intersections[i].second);

        if (diff < minDiff || (diff == minDiff && intersections[i + 1].first < minPosDiff)) {
            minDiff = diff;
            minPosDiff = intersections[i + 1].first;
            bestIndex = i;
        }
    }

    vector<int> selectedLines;
    for (int i = 0; i < lines.size(); i++) {
        if (onSegment(lines[bestIndex].x1, lines[bestIndex].y1, intersections[bestIndex].first, intersections[bestIndex].second, lines[i].x2, lines[i].y2)) {
            selectedLines.push_back(lines[i].index);
        }
    }

    return {minDiff, selectedLines};
}

int main() {
    int n;
    cin >> n;

    vector<Line> lines;

    for (int i = 0; i < n; i++) {
        int x1, y1, x2, y2;
        cin >> x1 >> y1 >> x2 >> y2;
        lines.push_back(Line(x1, y1, x2, y2, i + 1));
    }

    auto result = findBeautifulPoint(lines);

    cout << result.first << "\n";
    cout << result.second.size() << "\n";

    for (int index : result.second) {
        cout << index << " ";
    }

    return 0;
}