You are given three multisets of pairs of colored sticks: 

  * R pairs of red sticks, the first pair has length r_1, the second pair has length r_2, ..., the R-th pair has length r_R; 
  * G pairs of green sticks, the first pair has length g_1, the second pair has length g_2, ..., the G-th pair has length g_G; 
  * B pairs of blue sticks, the first pair has length b_1, the second pair has length b_2, ..., the B-th pair has length b_B; 



You are constructing rectangles from these pairs of sticks with the following process: 

  1. take a pair of sticks of one color; 
  2. take a pair of sticks of another color different from the first one; 
  3. add the area of the resulting rectangle to the total area. 



Thus, you get such rectangles that their opposite sides are the same color and their adjacent sides are not the same color.

Each pair of sticks can be used at most once, some pairs can be left unused. You are not allowed to split a pair into independent sticks.

What is the maximum area you can achieve?

Input

The first line contains three integers R, G, B (1 ≤ R, G, B ≤ 200) — the number of pairs of red sticks, the number of pairs of green sticks and the number of pairs of blue sticks.

The second line contains R integers r_1, r_2, ..., r_R (1 ≤ r_i ≤ 2000) — the lengths of sticks in each pair of red sticks.

The third line contains G integers g_1, g_2, ..., g_G (1 ≤ g_i ≤ 2000) — the lengths of sticks in each pair of green sticks.

The fourth line contains B integers b_1, b_2, ..., b_B (1 ≤ b_i ≤ 2000) — the lengths of sticks in each pair of blue sticks.

Output

Print the maximum possible total area of the constructed rectangles.

Examples

Input


1 1 1
3
5
4


Output


20


Input


2 1 3
9 5
1
2 8 5


Output


99


Input


10 1 1
11 7 20 15 19 14 2 4 13 14
8
11


Output


372

Note

In the first example you can construct one of these rectangles: red and green with sides 3 and 5, red and blue with sides 3 and 4 and green and blue with sides 5 and 4. The best area of them is 4 × 5 = 20.

In the second example the best rectangles are: red/blue 9 × 8, red/blue 5 × 5, green/blue 2 × 1. So the total area is 72 + 25 + 2 = 99.

In the third example the best rectangles are: red/green 19 × 8 and red/blue 20 × 11. The total area is 152 + 220 = 372. Note that you can't construct more rectangles because you are not allowed to have both pairs taken to be the same color.
import java.io.*;
import java.util.*;

public class Solution {

    private static boolean useInFile = false;
    private static boolean useOutFile = false;

    public static void main(String args[]) throws IOException {
        InOut inout = new InOut();
        Resolver resolver = new Resolver(inout);
        resolver.solve();
        inout.flush();
    }

    private static class Resolver {

        final long LONG_INF = (long) 1e18;
        final int INF = (int) (1e9 + 7);
        final int MOD = 998244353;
        long f[], inv[];
        InOut inout;

        Resolver(InOut inout) {
            this.inout = inout;
        }

        void initF(int n, int mod) {
            f = new long[n + 1];
            f[1] = 1;
            for (int i = 2; i <= n; i++) {
                f[i] = (f[i - 1] * i) % mod;
            }
        }

        void initInv(int n, int mod) {
            inv = new long[n + 1];
            inv[n] = pow(f[n], INF - 2, INF);
            for (int i = inv.length - 2; i >= 0; i--) {
                inv[i] = inv[i + 1] * (i + 1) % mod;
            }
        }

        long cmn(int n, int m, int mod) {
            return f[n] * inv[m] % mod * inv[n - m] % mod;
        }

        int d[] = {0, -1, 0, 1, 0};

        boolean legal(int r, int c, int n, int m) {
            return r >= 0 && r < n && c >= 0 && c < m;
        }

        void solve() throws IOException {
            int tt = 1;
            boolean hvt = false;
            if (hvt) {
                tt = nextInt();
//                tt = Integer.parseInt(nextLine());
            }
            for (int cs = 1; cs <= tt; cs++) {
                long rs = 0;
//                int n = nextInt();
                int R = nextInt();
                int G = nextInt();
                int B = nextInt();
                int r[] = anInt(0, R - 1);
                int g[] = anInt(0, G - 1);
                int b[] = anInt(0, B - 1);
                Arrays.sort(r);
                Arrays.sort(g);
                Arrays.sort(b);
                long dp[][][] = new long[202][202][202];
                dp[R][G - 1][B - 1] = g[G - 1] * b[B - 1];
                dp[R - 1][G][B - 1] = r[R - 1] * b[B - 1];
                dp[R - 1][G - 1][B] = r[R - 1] * g[G - 1];
                for (int i = R - 1; i >= 0; i--) {
                    for (int j = G - 1; j >= 0; j--) {
                        dp[i][j][B] = Math.max(dp[i + 1][j][B], dp[i][j + 1][B]);
                        dp[i][j][B] = Math.max(dp[i + 1][j + 1][B] + r[i] * g[j], dp[i][j][B]);
                    }
                }
                for (int i = R - 1; i >= 0; i--) {
                    for (int k = B - 1; k >= 0; k--) {
                        dp[i][G][k] = Math.max(dp[i + 1][G][k], dp[i][G][k + 1]);
                        dp[i][G][k] = Math.max(dp[i + 1][G][k + 1] + r[i] * b[k], dp[i][G][k]);
                    }
                }
                for (int j = G - 1; j >= 0; j--) {
                    for (int k = B - 1; k >= 0; k--) {
                        dp[R][j][k] = Math.max(dp[R][j + 1][k], dp[R][j][k + 1]);
                        dp[R][j][k] = Math.max(dp[R][j + 1][k + 1] + g[j] * b[k], dp[R][j][k]);
                    }
                }
                for (int i = R - 1; i >= 0; i--) {
                    for (int j = G - 1; j >= 0; j--) {
                        for (int k = B - 1; k >= 0; k--) {
                            dp[i][j][k] = Math.max(dp[i][j][k], dp[i + 1][j + 1][k] + r[i] * g[j]);
                            dp[i][j][k] = Math.max(dp[i][j][k], dp[i + 1][j][k + 1] + r[i] * b[k]);
                            dp[i][j][k] = Math.max(dp[i][j][k], dp[i][j + 1][k + 1] + g[j] * b[k]);
                            dp[i][j][k] = Math.max(dp[i][j][k], dp[i + 1][j][k]);
                            dp[i][j][k] = Math.max(dp[i][j][k], dp[i][j + 1][k]);
                            dp[i][j][k] = Math.max(dp[i][j][k], dp[i][j][k + 1]);
                            dp[i][j][k] = Math.max(dp[i][j][k], dp[i + 1][j + 1][k + 1]
                                    + Math.max(Math.max(r[i] * g[j], r[i] * b[k]), g[j] * b[k]));
                            rs = Math.max(rs, dp[i][j][k]);
                        }
                    }
                }

                format("%d", rs);
//                format("Case #%d: %d", cs, rs);

                if (cs < tt) {
                    format("\n");
                }
//                flush();
            }
        }

        private void updateSegTree(int n, long l, SegmentTree lft) {
            long lazy;
            lazy = 1;
            for (int j = 1; j <= l; j++) {
                lazy = (lazy + cmn((int) l, j, INF)) % INF;
                lft.modify(1, j, j, lazy);
            }
            lft.modify(1, (int) (l + 1), n, lazy);
        }

        String next() throws IOException {
            return inout.next();
        }

        String next(int n) throws IOException {
            return inout.next(n);
        }

        String nextLine() throws IOException {
            return inout.nextLine();
        }

        int nextInt() throws IOException {
            return inout.nextInt();
        }

        long nextLong(int n) throws IOException {
            return inout.nextLong(n);
        }

        int[] anInt(int i, int j) throws IOException {
            int a[] = new int[j + 1];
            for (int k = i; k <= j; k++) {
                a[k] = nextInt();
            }
            return a;
        }

        long[] anLong(int i, int j, int len) throws IOException {
            long a[] = new long[j + 1];
            for (int k = i; k <= j; k++) {
                a[k] = nextLong(len);
            }
            return a;
        }

        void print(String s, boolean nextLine) {
            inout.print(s, nextLine);
        }

        void format(String format, Object... obj) {
            inout.format(format, obj);
        }

        void flush() {
            inout.flush();
        }

        void swap(long a[], int i, int j) {
            a[i] ^= a[j];
            a[j] ^= a[i];
            a[i] ^= a[j];
        }

        int getP(int x, int p[]) {
            if (p[x] == 0 || p[x] == x) {
                return x;
            }
            return p[x] = getP(p[x], p);
        }

        void union(int x, int y, int p[]) {
            if (x < y) {
                p[y] = x;
            } else {
                p[x] = y;
            }
        }

        boolean topSort() {
            int n = adj2.length - 1;
            int d[] = new int[n + 1];
            for (int i = 1; i <= n; i++) {
                for (int j = 0; j < adj2[i].size(); j++) {
                    d[adj2[i].get(j)[0]]++;
                }
            }
            List<Integer> list = new ArrayList<>();
            for (int i = 1; i <= n; i++) {
                if (d[i] == 0) {
                    list.add(i);
                }
            }
            for (int i = 0; i < list.size(); i++) {
                for (int j = 0; j < adj2[list.get(i)].size(); j++) {
                    int t = adj2[list.get(i)].get(j)[0];
                    d[t]--;
                    if (d[t] == 0) {
                        list.add(t);
                    }
                }
            }
            return list.size() == n;
        }

        class SegmentTreeNode {
            long defaultVal = 0;
            int l, r;
            long val = defaultVal, lazy = defaultVal;

            SegmentTreeNode(int l, int r) {
                this.l = l;
                this.r = r;
            }
        }

        class SegmentTree {
            SegmentTreeNode tree[];
            long defaultVal = 0;
            long inf = Long.MIN_VALUE;
            long mod = INF;
            int type = 0;
            int MODIFY_VAL = 1;
            int MODIFY_LAZY = 2;
            int MODIFY_ALL = 3;

            SegmentTree(int n) {
                this(n, 0);
            }

            SegmentTree(int n, int type) {
                this.type = type;
                assert n > 0;
                tree = new SegmentTreeNode[n << 2];
            }

            SegmentTree build(int k, int l, int r) {
                if (l > r) {
                    return this;
                }
                if (null == tree[k]) {
                    tree[k] = new SegmentTreeNode(l, r);
                }
                if (l == r) {
                    return this;
                }
                int mid = (l + r) >> 1;
                build(k << 1, l, mid);
                build(k << 1 | 1, mid + 1, r);
                return this;
            }

            void pushDown(int k) {
                if (tree[k].l == tree[k].r) {
                    return;
                }
                long lazy = tree[k].lazy;
                modify(tree[k << 1], MODIFY_ALL, lazy);
                modify(tree[k << 1 | 1], MODIFY_ALL, lazy);
                tree[k].lazy = defaultVal;
            }

            void modify(int k, int l, int r, long val) {
                if (l > r) {
                    return;
                }
                if (tree[k].l >= l && tree[k].r <= r) {
                    modify(tree[k], MODIFY_ALL, val);
                    return;
                }
                int mid = (tree[k].l + tree[k].r) >> 1;
                if (mid >= l) {
                    modify(k << 1, l, r, val);
                }
                if (mid + 1 <= r) {
                    modify(k << 1 | 1, l, r, val);
                }
                tree[k].val = Math.max(tree[k << 1].val, tree[k << 1 | 1].val);
            }

            long query(int k, int l, int r) {
                if (tree[k].l > r || tree[k].r < l) {
                    return inf;
                }
                if (tree[k].lazy != defaultVal) {
                    pushDown(k);
                }
                if (tree[k].l >= l && tree[k].r <= r) {
                    return tree[k].val;
                }
                long ans = Math.max(query(k << 1, l, r), query(k << 1 | 1, l, r));
                if (tree[k].l < tree[k].r) {
                    tree[k].val = Math.max(tree[k << 1].val, tree[k << 1 | 1].val);
                }
                return ans;
            }

            private void modify(SegmentTreeNode node, int x, long val) {
                switch (type) {
                    case 0:
                        if (x == MODIFY_VAL) {
                            node.val += val;
                        } else if (x == MODIFY_LAZY) {
                            node.lazy += val;
                        } else {
                            node.val += val;
                            node.lazy += val;
                        }
                        break;
                    case 1:
                        if (x == MODIFY_VAL) {
                            node.val = node.val * val % mod;
                        } else if (x == MODIFY_LAZY) {
                            node.lazy = node.lazy * val % mod;
                        } else {
                            node.val = node.val * val % mod;
                            node.lazy = node.lazy * val % mod;
                        }
                        break;
                }
            }
        }

        class BinaryIndexedTree {

            int n = 1;
            long C[];

            BinaryIndexedTree(int sz) {
                while (n <= sz) {
                    n <<= 1;
                }
                C = new long[n];
            }

            int lowbit(int x) {
                return x & -x;
            }

            void add(int x, long val) {
                while (x < n) {
                    C[x] += val;
                    x += lowbit(x);
                }
            }

            long getSum(int x) {
                long res = 0;
                while (x > 0) {
                    res += C[x];
                    x -= lowbit(x);
                }
                return res;
            }

            int binSearch(long sum) {
                if (sum == 0) {
                    return 0;
                }
                int n = C.length;
                int mx = 1;
                while (mx < n) {
                    mx <<= 1;
                }
                int res = 0;
                for (int i = mx / 2; i >= 1; i >>= 1) {
                    if (C[res + i] < sum) {
                        sum -= C[res + i];
                        res += i;
                    }
                }
                return res + 1;
            }
        }

        int mnS;
        int mxS;
        Map<Integer, TrieNode> SS = new HashMap<>();

        class TrieNode {
            int cnt = 0;
            boolean isMin = false;
            boolean isMax = false;
            int mnIdx = 26;
            int mxIdx = -1;

            TrieNode next[];

            TrieNode() {
                next = new TrieNode[26];
            }

            private void insert(TrieNode trie, char ch[], int i, int j) {
                while (i < ch.length) {
                    int idx = ch[i] - 'a';
                    if (null == trie.next[idx]) {
                        trie.next[idx] = new TrieNode();
                    }
                    trie.cnt++;
                    int lastMnIdx = trie.mnIdx;
                    int lastMxIdx = trie.mxIdx;
                    trie.mnIdx = Math.min(trie.mnIdx, idx);
                    trie.mxIdx = Math.max(trie.mxIdx, idx);
                    if (trie.isMin && lastMnIdx != trie.mnIdx) {
                        if (lastMnIdx != 26) {
                            notMin(trie.next[lastMnIdx]);
                        }
                        trie.next[trie.mnIdx].isMin = true;
                    }
                    if (trie.isMax && lastMxIdx != trie.mxIdx) {
                        if (lastMxIdx >= 0) {
                            notMax(trie.next[lastMxIdx]);
                        }
                        trie.next[trie.mxIdx].isMax = true;
                    }
                    trie = trie.next[idx];
                    i++;
                }
                SS.put(j + 1, trie);
                if (trie.cnt == 0) {
                    if (trie.isMin) {
                        mnS = j + 1;
                    }
                    if (trie.isMax) {
                        mxS = j + 1;
                    }
                }
            }

            private void notMin(TrieNode trie) {
                while (null != trie) {
                    trie.isMin = false;
                    int val = trie.mnIdx;
                    if (val >= 26 || val < 0 || null == trie.next[val]) {
                        break;
                    }
                    trie = trie.next[val];
                }
            }

            private void notMax(TrieNode trie) {
                while (null != trie) {
                    trie.isMax = false;
                    int val = trie.mxIdx;
                    if (val >= 26 || val < 0 || null == trie.next[val]) {
                        break;
                    }
                    trie = trie.next[val];
                }
            }
        }

        //Binary tree
        class TreeNode {
            int val;
            int tier = -1;
            TreeNode parent;
            TreeNode left;
            TreeNode right;

            TreeNode(int val) {
                this.val = val;
            }
        }

        //binary tree dfs
        void tierTree(TreeNode root) {
            if (null == root) {
                return;
            }
            if (null != root.parent) {
                root.tier = root.parent.tier + 1;
            } else {
                root.tier = 0;
            }
            tierTree(root.left);
            tierTree(root.right);
        }

        //LCA start
        TreeNode[][] lca;
        TreeNode[] tree;

        void lcaDfsTree(TreeNode root) {
            if (null == root) {
                return;
            }
            tree[root.val] = root;
            TreeNode nxt = root.parent;
            int idx = 0;
            while (null != nxt) {
                lca[root.val][idx] = nxt;
                nxt = lca[nxt.val][idx];
                idx++;
            }
            lcaDfsTree(root.left);
            lcaDfsTree(root.right);
        }

        TreeNode lcaTree(TreeNode root, int n, TreeNode x, TreeNode y) throws IOException {
            if (null == root) {
                return null;
            }
            if (-1 == root.tier) {
                tree = new TreeNode[n + 1];
                tierTree(root);
            }
            if (null == lca) {
                lca = new TreeNode[n + 1][31];
                lcaDfsTree(root);
            }
            int z = Math.abs(x.tier - y.tier);
            int xx = x.tier > y.tier ? x.val : y.val;
            while (z > 0) {
                final int zz = z;
                int l = (int) BinSearch.bs(0, 31
                        , k -> zz < (1 << k));
                xx = lca[xx][l].val;
                z -= 1 << l;
            }
            int yy = y.val;
            if (x.tier <= y.tier) {
                yy = x.val;
            }
            while (xx != yy) {
                final int xxx = xx;
                final int yyy = yy;
                int l = (int) BinSearch.bs(0, 31
                        , k -> (1 << k) <= tree[xxx].tier && lca[xxx][(int) k] != lca[yyy][(int) k]);
                xx = lca[xx][l].val;
                yy = lca[yy][l].val;
            }
            return tree[xx];
        }
        //LCA end

        //graph
        List<Integer> adj[];
        List<int[]> adj2[];

        void initGraph(int n, int m, boolean hasW, boolean directed, int type) throws IOException {
            if (type == 1) {
                adj = new List[n + 1];
            } else {
                adj2 = new List[n + 1];
            }
            for (int i = 1; i <= n; i++) {
                if (type == 1) {
                    adj[i] = new ArrayList<>();
                } else {
                    adj2[i] = new ArrayList<>();
                }
            }
            for (int i = 0; i < m; i++) {
                int f = nextInt();
                int t = nextInt();
                if (type == 1) {
                    adj[f].add(t);
                    if (!directed) {
                        adj[t].add(f);
                    }
                } else {
                    int w = hasW ? nextInt() : 0;
                    adj2[f].add(new int[]{t, w});
                    if (!directed) {
                        adj2[t].add(new int[]{f, w});
                    }
                }
            }
        }

        void getDiv(Map<Integer, Integer> map, int n) {
            int sqrt = (int) Math.sqrt(n);
            for (int i = 2; i <= sqrt; i++) {
                int cnt = 0;
                while (n % i == 0) {
                    cnt++;
                    n /= i;
                }
                if (cnt > 0) {
                    map.put(i, cnt);
                }
            }
            if (n > 1) {
                map.put(n, 1);
            }
        }

        boolean[] generatePrime(int n) {
            boolean p[] = new boolean[n + 1];
            p[2] = true;

            for (int i = 3; i <= n; i += 2) {
                p[i] = true;
            }

            for (int i = 3; i <= Math.sqrt(n); i += 2) {
                if (!p[i]) {
                    continue;
                }
                for (int j = i * i; j <= n; j += i << 1) {
                    p[j] = false;
                }
            }
            return p;
        }

        boolean isPrime(long n) { //determines if n is a prime number
            int p[] = {2, 3, 5, 233, 331};
            int pn = p.length;
            long s = 0, t = n - 1;//n - 1 = 2^s * t
            while ((t & 1) == 0) {
                t >>= 1;
                ++s;
            }
            for (int i = 0; i < pn; ++i) {
                if (n == p[i]) {
                    return true;
                }
                long pt = pow(p[i], t, n);
                for (int j = 0; j < s; ++j) {
                    long cur = llMod(pt, pt, n);
                    if (cur == 1 && pt != 1 && pt != n - 1) {
                        return false;
                    }
                    pt = cur;
                }
                if (pt != 1) {
                    return false;
                }
            }
            return true;
        }

        long llMod(long a, long b, long mod) {
            return (a * b - (long) ((double) a / mod * b + 0.5) * mod + mod) % mod;
//        long r = 0;
//        a %= mod;
//        b %= mod;
//        while (b > 0) {
//            if ((b & 1) == 1) {
//                r = (r + a) % mod;
//            }
//            b >>= 1;
//            a = (a << 1) % mod;
//        }
//        return r;
        }

        long pow(long a, long n) {
            long ans = 1;
            while (n > 0) {
                if ((n & 1) == 1) {
                    ans = ans * a;
                }
                a = a * a;
                n >>= 1;
            }
            return ans;
        }

        long pow(long a, long n, long mod) {
            long ans = 1;
            while (n > 0) {
                if ((n & 1) == 1) {
                    ans = llMod(ans, a, mod);
                }
                a = llMod(a, a, mod);
                n >>= 1;
            }
            return ans;
        }

        private long[][] initC(int n) {
            long c[][] = new long[n][n];

            for (int i = 0; i < n; i++) {
                c[i][0] = 1;
            }

            for (int i = 1; i < n; i++) {
                for (int j = 1; j <= i; j++) {
                    c[i][j] = c[i - 1][j - 1] + c[i - 1][j];
                }
            }
            return c;
        }

        /**
         * ps: n >= m, choose m from n;
         */
//        private int cmn(long n, long m) {
//            if (m > n) {
//                n ^= m;
//                m ^= n;
//                n ^= m;
//            }
//            m = Math.min(m, n - m);
//
//            long top = 1;
//            long bot = 1;
//            for (long i = n - m + 1; i <= n; i++) {
//                top = (top * i) % MOD;
//            }
//            for (int i = 1; i <= m; i++) {
//                bot = (bot * i) % MOD;
//            }
//
//            return (int) ((top * pow(bot, MOD - 2, MOD)) % MOD);
//        }

        long gcd(long a, long b) {
            if (a < b) {
                return gcd(b, a);
            }
            while (b != 0) {
                long tmp = a % b;
                a = b;
                b = tmp;
            }
            return a;
        }

        int[] unique(int a[], Map<Integer, Integer> idx) {
            int tmp[] = a.clone();
            Arrays.sort(tmp);
            int j = 0;
            for (int i = 0; i < tmp.length; i++) {
                if (i == 0 || tmp[i] > tmp[i - 1]) {
                    idx.put(tmp[i], j++);
                }
            }
            int rs[] = new int[j];
            j = 0;
            for (int key : idx.keySet()) {
                rs[j++] = key;
            }
            Arrays.sort(rs);
            return rs;
        }

        boolean isEven(long n) {
            return (n & 1) == 0;
        }

        static class BinSearch {

            static long bs(long l, long r, IBinSearch sort) throws IOException {
                while (l < r) {
                    long m = l + (r - l) / 2;
                    if (sort.binSearchCmp(m)) {
                        l = m + 1;
                    } else {
                        r = m;
                    }
                }
                return l;
            }

            interface IBinSearch {
                boolean binSearchCmp(long k) throws IOException;
            }

        }
    }

    private static class InOut {
        private BufferedReader br;
        private StreamTokenizer st;
        private PrintWriter pw;

        InOut() throws FileNotFoundException {
            if (useInFile) {
                System.setIn(new FileInputStream("resources/inout/in.text"));
            }
            if (useOutFile) {
                System.setOut(new PrintStream("resources/inout/out.text"));
            }
            br = new BufferedReader(new InputStreamReader(System.in));
            st = new StreamTokenizer(br);
            pw = new PrintWriter(new OutputStreamWriter(System.out));
            st.ordinaryChar('\'');
            st.ordinaryChar('\"');
            st.ordinaryChar('/');
        }

        private long[] anLong(int n) throws IOException {
            long a[] = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        private String next() throws IOException {
            st.nextToken();
            return st.sval;
        }

        private String next(int len) throws IOException {
            char ch[] = new char[len];
            int cur = 0;
            char c;
            while ((c = (char) br.read()) == '\n' || c == '\r' || c == ' ' || c == '\t') ;
            do {
                ch[cur++] = c;
            } while (!((c = (char) br.read()) == '\n' || c == '\r' || c == ' ' || c == '\t'));
            return String.valueOf(ch, 0, cur);
        }

        private int nextInt() throws IOException {
            st.nextToken();
            return (int) st.nval;
        }

        private long nextLong(int n) throws IOException {
            return Long.parseLong(next(n));
        }

        private double nextDouble() throws IOException {
            st.nextToken();
            return st.nval;
        }

        private String[] nextSS(String reg) throws IOException {
            return br.readLine().split(reg);
        }

        private String nextLine() throws IOException {
            return br.readLine();
        }

        private void print(String s, boolean newLine) {
            if (null != s) {
                pw.print(s);
            }
            if (newLine) {
                pw.println();
            }
        }

        private void format(String format, Object... obj) {
            pw.format(format, obj);
        }

        private void flush() {
            pw.flush();
        }
    }

    private static class FFT {
        double[] roots;
        int maxN;

        public FFT(int maxN) {
            this.maxN = maxN;
            initRoots();
        }

        public long[] multiply(int[] a, int[] b) {
            int minSize = a.length + b.length - 1;
            int bits = 1;
            while (1 << bits < minSize) bits++;
            int N = 1 << bits;
            double[] aa = toComplex(a, N);
            double[] bb = toComplex(b, N);
            fftIterative(aa, false);
            fftIterative(bb, false);
            double[] c = new double[aa.length];
            for (int i = 0; i < N; i++) {
                c[2 * i] = aa[2 * i] * bb[2 * i] - aa[2 * i + 1] * bb[2 * i + 1];
                c[2 * i + 1] = aa[2 * i] * bb[2 * i + 1] + aa[2 * i + 1] * bb[2 * i];
            }
            fftIterative(c, true);
            long[] ret = new long[minSize];
            for (int i = 0; i < ret.length; i++) {
                ret[i] = Math.round(c[2 * i]);
            }
            return ret;
        }

        static double[] toComplex(int[] arr, int size) {
            double[] ret = new double[size * 2];
            for (int i = 0; i < arr.length; i++) {
                ret[2 * i] = arr[i];
            }
            return ret;
        }

        void initRoots() {
            roots = new double[2 * (maxN + 1)];
            double ang = 2 * Math.PI / maxN;
            for (int i = 0; i <= maxN; i++) {
                roots[2 * i] = Math.cos(i * ang);
                roots[2 * i + 1] = Math.sin(i * ang);
            }
        }

        int bits(int N) {
            int ret = 0;
            while (1 << ret < N) ret++;
            if (1 << ret != N) throw new RuntimeException();
            return ret;
        }

        void fftIterative(double[] array, boolean inv) {
            int bits = bits(array.length / 2);
            int N = 1 << bits;
            for (int from = 0; from < N; from++) {
                int to = Integer.reverse(from) >>> (32 - bits);
                if (from < to) {
                    double tmpR = array[2 * from];
                    double tmpI = array[2 * from + 1];
                    array[2 * from] = array[2 * to];
                    array[2 * from + 1] = array[2 * to + 1];
                    array[2 * to] = tmpR;
                    array[2 * to + 1] = tmpI;
                }
            }
            for (int n = 2; n <= N; n *= 2) {
                int delta = 2 * maxN / n;
                for (int from = 0; from < N; from += n) {
                    int rootIdx = inv ? 2 * maxN : 0;
                    double tmpR, tmpI;
                    for (int arrIdx = 2 * from; arrIdx < 2 * from + n; arrIdx += 2) {
                        tmpR = array[arrIdx + n] * roots[rootIdx] - array[arrIdx + n + 1] * roots[rootIdx + 1];
                        tmpI = array[arrIdx + n] * roots[rootIdx + 1] + array[arrIdx + n + 1] * roots[rootIdx];
                        array[arrIdx + n] = array[arrIdx] - tmpR;
                        array[arrIdx + n + 1] = array[arrIdx + 1] - tmpI;
                        array[arrIdx] += tmpR;
                        array[arrIdx + 1] += tmpI;
                        rootIdx += (inv ? -delta : delta);
                    }
                }
            }
            if (inv) {
                for (int i = 0; i < array.length; i++) {
                    array[i] /= N;
                }
            }
        }
    }
}