Problem: It is Bubble Cup finals season and farmer Johnny Bubbles must harvest his bubbles. The bubbles are in a rectangular bubblefield formed of N x M square parcels divided into N rows and M columns. The parcel in i^{th} row and j^{th} column yields A_{i,j} bubbles.

Johnny Bubbles has available a very special self-driving bubble harvester that, once manually positioned at the beginning of a row or column, automatically harvests all the bubbles in that row or column. Once the harvester reaches the end of the row or column it stops and must be repositioned. The harvester can pass through any parcel any number of times, but it can collect bubbles from the parcel only once.

Johnny is very busy farmer, so he is available to manually position the harvester at most four times per day. Johnny is also impatient, so he wants to harvest as many bubbles as possible on the first day.

Please help Johnny to calculate what is the maximum number of bubbles he can collect on the first day.

Input

The first line contains two integers N and M (1 ≤ N, M ≤ N * M ≤ 10^{5}) - the bubblefield size.

Each of the next N lines contains M integers. The j^{th} element in the i^{th} line is A_{i,j} (0 ≤ a_{i,j} ≤ 10^{9}) — the yield of the parcel located in the i^{th} row and the j^{th} column.

Output

Output contains one integer number - maximum number of the bubbles Johnny can harvest on the first day.

Examples

Input


2 2
1 2
3 4


Output


10


Input


5 5
0 9 2 7 0
9 0 3 0 5
0 8 0 3 1
6 7 4 3 9
3 6 4 1 0


Output


80

Note

In the first example, farmer Johnny can harvest all the bubbles by positioning the harvester on the first and the second row.

In the second example, one way Johnny can harvest maximum number of bubbles is to position the harvester in the second row, the fourth row, the second column and the fourth column.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

import static java.lang.Math.*;
import static java.util.Arrays.*;

public class cf1219g {

    public static void main(String[] args) throws IOException {
        int n = rni(), m = ni(), a[][] = new int[min(n, m)][max(n, m)];
        if (n < m) {
            for (int i = 0; i < n; ++i) {
                r();
                for (int j = 0; j < m; ++j) {
                    a[i][j] = ni();
                }
            }
        } else {
            for (int i = 0; i < n; ++i) {
                r();
                for (int j = 0; j < m; ++j) {
                    a[j][i] = ni();
                }
            }
            int __swap = n;
            n = m;
            m = __swap;
        }
        if (n <= 4) {
            long ans = 0;
            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < m; ++j) {
                    ans += a[i][j];
                }
            }
            prln(ans);
            close();
            return;
        }
        long ans = 0;
        // greedy 4 rows / 4 cols
        long[] row_sums = new long[n], col_sums = new long[m], sorted;
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < m; ++j) {
                row_sums[i] += a[i][j];
                col_sums[j] += a[i][j];
            }
        }
        ans = max(sum_max(row_sums, 4), sum_max(col_sums, 4));
        // 1 row
        for (int i = 0; i < n; ++i) {
            long sum = 0;
            for (int j = 0; j < m; ++j) {
                col_sums[j] -= a[i][j];
            }
            ans = max(ans, sum + sum_max(col_sums, 3));
            for (int j = 0; j < m; ++j) {
                col_sums[j] += a[i][j];
            }
        }
        // 2 rows
        for (int i = 0; i < n - 1; ++i) {
            long sum1 = 0;
            for (int j = 0; j < m; ++j) {
                sum1 += a[i][j];
                col_sums[j] -= a[i][j];
            }
            for (int j = i + 1; j < n; ++j) {
                long sum2 = 0;
                for (int k = 0; k < m; ++k) {
                    sum2 += a[j][k];
                    col_sums[k] -= a[j][k];
                }
                ans = max(ans, sum1 + sum2 + sum_max(col_sums, 2));
                for (int k = 0; k < m; ++k) {
                    col_sums[k] += a[j][k];
                }
            }
            for (int j = 0; j < m; ++j) {
                col_sums[j] += a[i][j];
            }
        }
        // 1 col
        for (int j = 0; j < m; ++j) {
            long sum = 0;
            for (int i = 0; i < n; ++i) {
                sum += a[i][j];
                row_sums[i] -= a[i][j];
            }
            ans = max(ans, sum + sum_max(row_sums, 3));
            for (int i = 0; i < n; ++i) {
                row_sums[i] += a[i][j];
            }
        }
        prln(ans);
        close();
    }

    static long sum_max(long[] a, int num) {
        long ans = 0, arr[] = copy(a);
        while (num --> 0) {
            long max = 0;
            int ind = -1;
            for (int i = 0; i < arr.length; ++i) {
                if (arr[i] > max) {
                    max = arr[i];
                    ind = i;
                }
            }
            ans += max;
            arr[ind] = 0;
        }
        return ans;
    }

    @FunctionalInterface
    interface LongOperator {
        long merge(long a, long b);
    }

    static class sgt {
        LongOperator upd_op, qry_op;
        int n;
        long sgt[], id;

        sgt(int sz, LongOperator operator, long identity) {
            n = sz;
            sgt = new long[4 * n + 5];
            upd_op = qry_op = operator;
            id = identity;
        }

        sgt(int sz, LongOperator update_operator, LongOperator query_operator, long identity) {
            n = sz;
            sgt = new long[4 * n + 5];
            upd_op = update_operator;
            qry_op = query_operator;
            id = identity;
        }

        sgt(long[] a, LongOperator operator, long identity) {
            n = a.length;
            sgt = new long[4 * n + 5];
            upd_op = qry_op = operator;
            id = identity;
            build(1, a, 0, n - 1);
        }

        sgt(long[] a, LongOperator update_operator, LongOperator query_operator, long identity) {
            n = a.length;
            sgt = new long[4 * n + 5];
            upd_op = update_operator;
            qry_op = query_operator;
            id = identity;
            build(1, a, 0, n - 1);
        }

        void set(int i, long x) {
            set(1, i, x, 0, n - 1);
        }

        void upd(int i, long x) {
            upd(1, i, x, 0, n - 1);
        }

        long qry(int l, int r) {
            return qry(1, l, r - 1, 0, n - 1);
        }

        void set(int node, int i, long x, int l, int r) {
            if (l == r) {
                sgt[node] = x;
            } else {
                int m = l + (r - l) / 2;
                if (i <= m) {
                    set(node << 1, i, x, l, m);
                } else {
                    set(node << 1 | 1, i, x, m + 1, r);
                }
                pull(node);
            }
        }

        void upd(int node, int i, long x, int l, int r) {
            if (l == r) {
                sgt[node] = upd_op.merge(sgt[node], x);
            } else {
                int m = l + (r - l) / 2;
                if (i <= m) {
                    upd(node << 1, i, x, l, m);
                } else {
                    upd(node << 1 | 1, i, x, m + 1, r);
                }
                pull(node);
            }
        }

        long qry(int node, int i, int j, int l, int r) {
            if (r < i || j < l) {
                return id;
            } else if (i <= l && r <= j) {
                return sgt[node];
            } else {
                int m = l + (r - l) / 2;
                return qry_op.merge(qry(node << 1, i, j, l, m), qry(node << 1 | 1, i, j, m + 1, r));
            }
        }

        void build(int node, long[] a, int l, int r) {
            if (l == r) {
                sgt[node] = a[l];
            } else {
                int m = l + (r - l) / 2;
                build(node << 1, a, l, m);
                build(node << 1 | 1, a, m + 1, r);
                pull(node);
            }
        }

        void pull(int node) {
            sgt[node] = qry_op.merge(sgt[node << 1], sgt[node << 1 | 1]);
        }
    }

    static BufferedReader __in = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter __out = new PrintWriter(new OutputStreamWriter(System.out));
    static StringTokenizer input;
    static Random __rand = new Random();

    // references
    // IBIG = 1e9 + 7
    // IMAX ~= 2e9
    // LMAX ~= 9e18

    // constants
    static final int IBIG = 1000000007;
    static final int IMAX = 2147483647;
    static final int IMIN = -2147483648;
    static final long LMAX = 9223372036854775807L;
    static final long LMIN = -9223372036854775808L;
    // math util
    static int minof(int a, int b, int c) {return min(a, min(b, c));}
    static int minof(int... x) {if (x.length == 1) return x[0]; if (x.length == 2) return min(x[0], x[1]); if (x.length == 3) return min(x[0], min(x[1], x[2])); int min = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i]; return min;}
    static long minof(long a, long b, long c) {return min(a, min(b, c));}
    static long minof(long... x) {if (x.length == 1) return x[0]; if (x.length == 2) return min(x[0], x[1]); if (x.length == 3) return min(x[0], min(x[1], x[2])); long min = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i]; return min;}
    static int maxof(int a, int b, int c) {return max(a, max(b, c));}
    static int maxof(int... x) {if (x.length == 1) return x[0]; if (x.length == 2) return max(x[0], x[1]); if (x.length == 3) return max(x[0], max(x[1], x[2])); int max = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i]; return max;}
    static long maxof(long a, long b, long c) {return max(a, max(b, c));}
    static long maxof(long... x) {if (x.length == 1) return x[0]; if (x.length == 2) return max(x[0], x[1]); if (x.length == 3) return max(x[0], max(x[1], x[2])); long max = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i]; return max;}
    static int powi(int a, int b) {if (a == 0) return 0; int ans = 1; while (b > 0) {if ((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
    static long powl(long a, int b) {if (a == 0) return 0; long ans = 1; while (b > 0) {if ((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
    static int fli(double d) {return (int) d;}
    static int cei(double d) {return (int) ceil(d);}
    static long fll(double d) {return (long) d;}
    static long cel(double d) {return (long) ceil(d);}
    static int gcf(int a, int b) {return b == 0 ? a : gcf(b, a % b);}
    static long gcf(long a, long b) {return b == 0 ? a : gcf(b, a % b);}
    static int lcm(int a, int b) {return a * b / gcf(a, b);}
    static long lcm(long a, long b) {return a * b / gcf(a, b);}
    static int randInt(int min, int max) {return __rand.nextInt(max - min + 1) + min;}
    static long mix(long x) {x += 0x9e3779b97f4a7c15L; x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9L; x = (x ^ (x >> 27)) * 0x94d049bb133111ebL; return x ^ (x >> 31);}
    // array util
    static void reverse(int[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {int swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void reverse(long[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {long swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void reverse(double[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {double swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void reverse(char[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {char swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void shuffle(int[] a) {int n = a.length - 1; for (int i = 0; i < n; ++i) {int ind = randInt(i, n); int swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
    static void shuffle(long[] a) {int n = a.length - 1; for (int i = 0; i < n; ++i) {int ind = randInt(i, n); long swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
    static void shuffle(double[] a) {int n = a.length - 1; for (int i = 0; i < n; ++i) {int ind = randInt(i, n); double swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
    static void rsort(int[] a) {shuffle(a); sort(a);}
    static void rsort(long[] a) {shuffle(a); sort(a);}
    static void rsort(double[] a) {shuffle(a); sort(a);}
    static int[] copy(int[] a) {int[] ans = new int[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    static long[] copy(long[] a) {long[] ans = new long[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    static double[] copy(double[] a) {double[] ans = new double[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    static char[] copy(char[] a) {char[] ans = new char[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    // graph util
    static List<List<Integer>> g(int n) {List<List<Integer>> g = new ArrayList<>(); for (int i = 0; i < n; ++i) g.add(new ArrayList<>()); return g;}
    static List<Set<Integer>> sg(int n) {List<Set<Integer>> g = new ArrayList<>(); for (int i = 0; i < n; ++i) g.add(new HashSet<>()); return g;}
    static void c(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).add(v); g.get(v).add(u);}
    static void cto(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).add(v);}
    static void dc(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).remove(v); g.get(v).remove(u);}
    static void dcto(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).remove(v);}
    // input
    static void r() throws IOException {input = new StringTokenizer(rline());}
    static int ri() throws IOException {return Integer.parseInt(rline());}
    static long rl() throws IOException {return Long.parseLong(rline());}
    static double rd() throws IOException {return Double.parseDouble(rline());}
    static int[] ria(int n) throws IOException {int[] a = new int[n]; r(); for (int i = 0; i < n; ++i) a[i] = ni(); return a;}
    static int[] riam1(int n) throws IOException {int[] a = new int[n]; r(); for (int i = 0; i < n; ++i) a[i] = ni() - 1; return a;}
    static long[] rla(int n) throws IOException {long[] a = new long[n]; r(); for (int i = 0; i < n; ++i) a[i] = nl(); return a;}
    static double[] rda(int n) throws IOException {double[] a = new double[n]; r(); for (int i = 0; i < n; ++i) a[i] = nd(); return a;}
    static char[] rcha() throws IOException {return rline().toCharArray();}
    static String rline() throws IOException {return __in.readLine();}
    static String n() {return input.nextToken();}
    static int rni() throws IOException {r(); return ni();}
    static int ni() {return Integer.parseInt(n());}
    static long rnl() throws IOException {r(); return nl();}
    static long nl() {return Long.parseLong(n());}
    static double rnd() throws IOException {r(); return nd();}
    static double nd() {return Double.parseDouble(n());}
    static List<List<Integer>> rg(int n, int m) throws IOException {List<List<Integer>> g = g(n); for (int i = 0; i < m; ++i) c(g, rni() - 1, ni() - 1); return g;}
    static void rg(List<List<Integer>> g, int m) throws IOException {for (int i = 0; i < m; ++i) c(g, rni() - 1, ni() - 1);}
    static List<List<Integer>> rdg(int n, int m) throws IOException {List<List<Integer>> g = g(n); for (int i = 0; i < m; ++i) cto(g, rni() - 1, ni() - 1); return g;}
    static void rdg(List<List<Integer>> g, int m) throws IOException {for (int i = 0; i < m; ++i) cto(g, rni() - 1, ni() - 1);}
    static List<Set<Integer>> rsg(int n, int m) throws IOException {List<Set<Integer>> g = sg(n); for (int i = 0; i < m; ++i) c(g, rni() - 1, ni() - 1); return g;}
    static void rsg(List<Set<Integer>> g, int m) throws IOException {for (int i = 0; i < m; ++i) c(g, rni() - 1, ni() - 1);}
    static List<Set<Integer>> rdsg(int n, int m) throws IOException {List<Set<Integer>> g = sg(n); for (int i = 0; i < m; ++i) cto(g, rni() - 1, ni() - 1); return g;}
    static void rdsg(List<Set<Integer>> g, int m) throws IOException {for (int i = 0; i < m; ++i) cto(g, rni() - 1, ni() - 1);}
    // output
    static void pr(int i) {__out.print(i);}
    static void prln(int i) {__out.println(i);}
    static void pr(long l) {__out.print(l);}
    static void prln(long l) {__out.println(l);}
    static void pr(double d) {__out.print(d);}
    static void prln(double d) {__out.println(d);}
    static void pr(char c) {__out.print(c);}
    static void prln(char c) {__out.println(c);}
    static void pr(char[] s) {__out.print(new String(s));}
    static void prln(char[] s) {__out.println(new String(s));}
    static void pr(String s) {__out.print(s);}
    static void prln(String s) {__out.println(s);}
    static void pr(Object o) {__out.print(o);}
    static void prln(Object o) {__out.println(o);}
    static void prln() {__out.println();}
    static void pryes() {prln("yes");}
    static void pry() {prln("Yes");}
    static void prY() {prln("YES");}
    static void prno() {prln("no");}
    static void prn() {prln("No");}
    static void prN() {prln("NO");}
    static void pryesno(boolean b) {prln(b ? "yes" : "no");};
    static void pryn(boolean b) {prln(b ? "Yes" : "No");}
    static void prYN(boolean b) {prln(b ? "YES" : "NO");}
    static void prln(int... a) {for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i); if (a.length > 0) prln(a[a.length - 1]); else prln();}
    static void prln(long... a) {for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i); if (a.length > 0) prln(a[a.length - 1]); else prln();}
    static void prln(double... a) {for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i); if (a.length > 0) prln(a[a.length - 1]); else prln();}
    static <T> void prln(Collection<T> c) {int n = c.size() - 1; Iterator<T> iter = c.iterator(); for (int i = 0; i < n; pr(iter.next()), pr(' '), ++i); if (n >= 0) prln(iter.next()); else prln();}
    static void h() {prln("hlfd"); flush();}
    static void flush() {__out.flush();}
    static void close() {__out.close();}}