Karen and Cards

题意翻译

给n个三元组，再构造一个三元组(a,b,c),a<=p,b<=q,c<=r 求有多少个满足，a,b,c中至少两个大于每一个a[i],b[i],c[i]

题目描述

Karen just got home from the supermarket, and is getting ready to go to sleep. After taking a shower and changing into her pajamas, she looked at her shelf and saw an album. Curious, she opened it and saw a trading card collection. She recalled that she used to play with those cards as a child, and, although she is now grown-up, she still wonders a few things about it. Each card has three characteristics: strength, defense and speed. The values of all characteristics of all cards are positive integers. The maximum possible strength any card can have is $ p $ , the maximum possible defense is $ q $ and the maximum possible speed is $ r $ . There are $ n $ cards in her collection. The $ i $ -th card has a strength $ a_{i} $ , defense $ b_{i} $ and speed $ c_{i} $ , respectively. A card beats another card if at least two of its characteristics are strictly greater than the corresponding characteristics of the other card. She now wonders how many different cards can beat all the cards in her collection. Two cards are considered different if at least one of their characteristics have different values.

输入输出格式

输入格式

The first line of input contains four integers, $ n $ , $ p $ , $ q $ and $ r $ ( $ 1<=n,p,q,r<=500000 $ ), the number of cards in the collection, the maximum possible strength, the maximum possible defense, and the maximum possible speed, respectively. The next $ n $ lines each contain three integers. In particular, the $ i $ -th line contains $ a_{i} $ , $ b_{i} $ and $ c_{i} $ ( $ 1<=a_{i}<=p $ , $ 1<=b_{i}<=q $ , $ 1<=c_{i}<=r $ ), the strength, defense and speed of the $ i $ -th collection card, respectively.

输出格式

Output a single integer on a line by itself, the number of different cards that can beat all the cards in her collection.

输入输出样例

输入样例 #1

3 4 4 5
2 2 5
1 3 4
4 1 1

输出样例 #1

10

输入样例 #2

5 10 10 10
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1

输出样例 #2

972

说明

In the first test case, the maximum possible strength is $ 4 $ , the maximum possible defense is $ 4 $ and the maximum possible speed is $ 5 $ . Karen has three cards: - The first card has strength $ 2 $ , defense $ 2 $ and speed $ 5 $ . - The second card has strength $ 1 $ , defense $ 3 $ and speed $ 4 $ . - The third card has strength $ 4 $ , defense $ 1 $ and speed $ 1 $ . There are $ 10 $ cards that beat all the cards here: 1. The card with strength $ 3 $ , defense $ 3 $ and speed $ 5 $ . 2. The card with strength $ 3 $ , defense $ 4 $ and speed $ 2 $ . 3. The card with strength $ 3 $ , defense $ 4 $ and speed $ 3 $ . 4. The card with strength $ 3 $ , defense $ 4 $ and speed $ 4 $ . 5. The card with strength $ 3 $ , defense $ 4 $ and speed $ 5 $ . 6. The card with strength $ 4 $ , defense $ 3 $ and speed $ 5 $ . 7. The card with strength $ 4 $ , defense $ 4 $ and speed $ 2 $ . 8. The card with strength $ 4 $ , defense $ 4 $ and speed $ 3 $ . 9. The card with strength $ 4 $ , defense $ 4 $ and speed $ 4 $ . 10. The card with strength $ 4 $ , defense $ 4 $ and speed $ 5 $ . In the second test case, the maximum possible strength is $ 10 $ , the maximum possible defense is $ 10 $ and the maximum possible speed is $ 10 $ . Karen has five cards, all with strength $ 1 $ , defense $ 1 $ and speed $ 1 $ . Any of the $ 972 $ cards which have at least two characteristics greater than $ 1 $ can beat all of the cards in her collection.

题意翻译

有 $n$ 张卡牌，每张卡牌都有三个属性，第 $i$ 张卡牌的三个属性记作 $a_i,b_i,c_i$。卡牌 $x$ 可以打败卡牌 $y$ 当且仅当 $x$ 至少有两个属性值比 $y$ 对应的属性值大。如卡牌 $(1,2,3)$ 可以打败卡牌 $(3,1,2)$，因为 $2>1,3>2$。 现在请你判断满足 $a\leq p,b\leq q, c\leq r$ 的卡牌中，可以打败给定的所有 $n$ 张卡牌的有多少张。