CF1861F.Four Suits

The game of Berland poker is played as follows. There are $n+1$ people: $n$ players, numbered from $1$ to $n$, and the dealer. The dealer has a deck which contains cards of four different suits (the number of cards of each suit is not necessarily the same); the number of cards in the deck is divisible by $n$. The dealer gives all cards to the players, so that every player receives the same number of cards, and the whole deck is used.

After the cards are dealt, every player chooses one of four suits (independently) and discards all cards from their hand which do not belong to their chosen suit. The winner of the game is the player with the maximum number of cards left in their hand. The number of points the winner receives is $x - y$, where $x$ is the number of cards in the winner's hand, and $y$ is the maximum number of cards among all other players; everyone else receives $0$ points. Note that it means that if there are multiple players with the maximum number of cards, everyone receives $0$ points.

Since every player wants to maximize their odds to win, they will choose a suit with the maximum number of cards in their hand.

Monocarp is the dealer. He has already given some cards to the players; the $i$-th player received $a_{i,j}$ cards of suit $j$. Note that the number of cards in players' hands don't have to be the same at this moment. Monocarp has $b_1, b_2, b_3, b_4$ cards of suit $1, 2, 3, 4$ respectively left in his deck. He has to give them to the players so that, after all cards are dealt, every player has the same number of cards.

For each player, calculate the maximum number of points they can receive among all ways to deal the remaining cards according to the rules of the game.

伯兰德扑克（Berland poker）游戏规则如下：共有 $n+1$ 人，其中 $n$ 名玩家（编号为 $1$ 至 $n$）和一名庄家。庄家拥有一副牌，牌面共分四种花色（每种花色的牌数不一定相等）；整副牌的总张数能被 $n$ 整除。庄家将所有牌发给玩家，使得每位玩家获得相同数量的牌，且整副牌全部发完。

发牌结束后，每位玩家独立地从四种花色中选择一种，并弃掉手中所有不属于所选花色的牌。游戏的获胜者是手中剩余牌数最多的玩家。获胜者所得分数为 $x - y$，其中 $x$ 是获胜者手中剩余的牌数，$y$ 是其余所有玩家中剩余牌数的最大值；其余所有玩家均得 $0$ 分。注意：若存在多名玩家手中剩余牌数并列最多，则所有玩家均得 $0$ 分。

由于每位玩家都希望最大化自己获胜的概率，因此他们总会选择自己手中数量最多的那种花色（若有多种花色数量相同且均为最大，则任选其一）。

Monocarp 是庄家。他已向各位玩家发出部分牌：第 $i$ 位玩家已收到花色 $j$ 的牌 $a_{i,j}$ 张。注意：此时各位玩家手中的牌数未必相等。Monocarp 的牌堆中还剩下 $b_1, b_2, b_3, b_4$ 张花色分别为 $1, 2, 3, 4$ 的牌。他必须将这些剩余的牌全部发给玩家，使得最终每位玩家手中的总牌数完全相等。

对每位玩家，请计算在所有符合游戏规则的剩余发牌方案中，该玩家所能获得的最高分数。

The first line of the input contains one integer $n$ ($2 \le n \le 5 \cdot 10^4$) — the number of players.

Then $n$ lines follow. The $i$-th of them contains four integers $a_{i,1}, a_{i,2}, a_{i,3}, a_{i,4}$ ($0 \le a_{i,j} \le 10^6$), where $a_{i,j}$ is the number of cards of the $j$-th suit that the $i$-th player currently has.

The last line contains $4$ integers $b_1, b_2, b_3, b_4$ ($0 \le b_j \le 10^6$), where $b_j$ is the number of cards of the $j$-th suit Monocarp has to deal yet.

Additional constraint on the input: it is possible to deal all of the remaining cards so that every player has the same number of cards.

输入的第一行包含一个整数 $n$（$2 \le n \le 5 \cdot 10^4$），表示玩家数量。

接下来是 $n$ 行。其中第 $i$ 行包含四个整数 $a_{i,1}, a_{i,2}, a_{i,3}, a_{i,4}$（$0 \le a_{i,j} \le 10^6$），其中 $a_{i,j}$ 表示第 $i$ 位玩家当前持有的第 $j$ 种花色的牌的数量。

最后一行包含四个整数 $b_1, b_2, b_3, b_4$（$0 \le b_j \le 10^6$），其中 $b_j$ 表示 Monocarp 尚需分发的第 $j$ 种花色的牌的数量。

输入的附加约束：可以将所有剩余的牌全部分发完毕，使得每位玩家最终持有的牌数相等。

Print $n$ integers. The $i$-th of them should be the maximum number of points the $i$-th player can get among all possible ways to deal the remaining cards.

输出 $n$ 个整数。其中第 $i$ 个整数应为：在所有可能的剩余牌分配方式中，第 $i$ 个玩家所能获得的最大点数。