CF1010E.Store

Natasha was already going to fly back to Earth when she remembered that she needs to go to the Martian store to buy Martian souvenirs for her friends.

It is known, that the Martian year lasts $x_{max}$ months, month lasts $y_{max}$ days, day lasts $z_{max}$ seconds. Natasha also knows that this store works according to the following schedule: 2 months in a year were selected: $x_l$ and $x_r$ ($1\le x_l\le x_r\le x_{max}$), 2 days in a month: $y_l$ and $y_r$ ($1\le y_l\le y_r\le y_{max}$) and 2 seconds in a day: $z_l$ and $z_r$ ($1\le z_l\le z_r\le z_{max}$). The store works at all such moments (month $x$, day $y$, second $z$), when simultaneously $x_l\le x\le x_r$, $y_l\le y\le y_r$ and $z_l\le z\le z_r$.

Unfortunately, Natasha does not know the numbers $x_l,x_r,y_l,y_r,z_l,z_r$.

One Martian told Natasha: "I went to this store $(n+m)$ times. $n$ times of them it was opened, and $m$ times — closed." He also described his every trip to the store: the month, day, second of the trip and whether the store was open or closed at that moment.

Natasha can go to the store $k$ times. For each of them, determine whether the store at the time of the trip is open, closed, or this information is unknown.

娜塔莎正准备返回地球，突然想起她需要去火星商店为朋友们购买火星纪念品。

已知：火星一年持续 $x_{max}$ 个月，一个月持续 $y_{max}$ 天，一天持续 $z_{max}$ 秒。娜塔莎还知道该商店按如下时间表营业：一年中选定两个月份 $x_l$ 和 $x_r$（满足 $1\le x_l\le x_r\le x_{max}$），一月中选定两天 $y_l$ 和 $y_r$（满足 $1\le y_l\le y_r\le y_{max}$），一天中选定两秒 $z_l$ 和 $z_r$（满足 $1\le z_l\le z_r\le z_{max}$）。商店在所有满足 $x_l\le x\le x_r$、$y_l\le y\le y_r$ 且 $z_l\le z\le z_r$ 的时刻（即月份 $x$、日期 $y$、秒数 $z$）营业。

不幸的是，娜塔莎并不知道参数 $x_l,x_r,y_l,y_r,z_l,z_r$ 的具体取值。

一位火星人告诉娜塔莎：“我去过这家商店 $(n+m)$ 次，其中 $n$ 次商店是营业的，$m$ 次是关闭的。” 他还详细描述了每次前往商店的情况：包括前往时的月份、日期、秒数，以及当时商店是营业还是关闭。

娜塔莎可以再去商店 $k$ 次。对于这 $k$ 次中的每一次，请判断：在该次前往的时刻，商店是营业的、关闭的，还是无法确定。

The first line contains $6$ integers $x_{max}$, $y_{max}$, $z_{max}$, $n$, $m$, $k$ ($1\le x_{max},y_{max},z_{max}\le 10^5$, $1\le n\le 10^5$, $0\le m\le 10^5$, $1\le k\le 10^5$) — number of months in a year, days in a month, seconds in a day, times when the store (according to a Martian) was opened, when it was closed and Natasha's queries.

The $i$-th of the next $n$ lines contains $3$ integers $x_i$, $y_i$, $z_i$ ($1\le x_i\le x_{max}$, $1\le y_i\le y_{max}$, $1\le z_i\le z_{max}$) — month, day and second of $i$-th time, when the store, according to the Martian, was opened.

The $i$-th of the next $m$ lines contains $3$ integers $x_i$, $y_i$, $z_i$ ($1\le x_i\le x_{max}$, $1\le y_i\le y_{max}$, $1\le z_i\le z_{max}$) — month, day and second of $i$-th time, when the store, according to the Martian, was closed.

The $i$-th of the next $k$ lines contains $3$ integers $x_i$, $y_i$, $z_i$ ($1\le x_i\le x_{max}$, $1\le y_i\le y_{max}$, $1\le z_i\le z_{max}$) — month, day and second of $i$-th Natasha's query.

第一行包含 $6$ 个整数 $x_{max}$、$y_{max}$、$z_{max}$、$n$、$m$、$k$（$1\le x_{max},y_{max},z_{max}\le 10^5$，$1\le n\le 10^5$，$0\le m\le 10^5$，$1\le k\le 10^5$）—— 分别表示一年中的月份数、一月中的天数、一天中的秒数、火星人记录的商店开业次数、关门次数以及娜塔莎的查询次数。

接下来 $n$ 行中的第 $i$ 行包含 $3$ 个整数 $x_i$、$y_i$、$z_i$（$1\le x_i\le x_{max}$，$1\le y_i\le y_{max}$，$1\le z_i\le z_{max}$）—— 表示火星人记录的第 $i$ 次商店开业时间的月份、日期和秒数。

接下来 $m$ 行中的第 $i$ 行包含 $3$ 个整数 $x_i$、$y_i$、$z_i$（$1\le x_i\le x_{max}$，$1\le y_i\le y_{max}$，$1\le z_i\le z_{max}$）—— 表示火星人记录的第 $i$ 次商店关门时间的月份、日期和秒数。

接下来 $k$ 行中的第 $i$ 行包含 $3$ 个整数 $x_i$、$y_i$、$z_i$（$1\le x_i\le x_{max}$，$1\le y_i\le y_{max}$，$1\le z_i\le z_{max}$）—— 表示娜塔莎的第 $i$ 次查询时间的月份、日期和秒数。

If the Martian was mistaken and his information about when the store is open and when it is closed is inconsistent, print a single line "INCORRECT" (without quotes).

Otherwise, print the first line "CORRECT" (without quotes). Next output $k$ lines: in $i$-th of them, output an answer to $i$-th Natasha's query: "OPEN" (without quotes), if the store was opened at the moment of this query, "CLOSED" (without quotes), if it was closed, or "UNKNOWN" (without quotes), if this information can not be determined on the basis of available data.

如果火星人弄错了，且他关于商店营业和关门时间的信息存在矛盾，则输出一行 "INCORRECT"（不带引号）。

否则，第一行输出 "CORRECT"（不带引号）。接下来输出 $k$ 行：其中第 $i$ 行为娜塔莎的第 $i$ 个查询的答案——若在该查询时刻商店处于营业状态，则输出 "OPEN"（不带引号）；若处于关门状态，则输出 "CLOSED"（不带引号）；若根据现有数据无法确定，则输出 "UNKNOWN"（不带引号）。

Consider the first test case.

There are $10$ months in a year, $10$ days in a month, and $10$ seconds in a day.

The store was opened in $3$ moments:

• month $2$, day $6$, second $2$;
• month $4$, day $2$, second $4$;
• month $6$, day $4$, second $6$.

The store was closed at the time: month $9$, day $9$, second $9$.

Queries:

• month $3$, day $3$, second $3$ — open ("OPEN") (since the store opens no later than month $2$, day $2$, second $2$ and closes no earlier than in month $6$, day $6$, second $6$);
• month $10$, day $10$, second $10$ — closed ("CLOSED") (since it is closed even in the month $9$, day $9$, second $9$);
• month $8$, day $8$, second $8$ — unknown ("UNKNOWN") (because the schedule in which the store is open at this moment exists, and the schedule in which the store is closed at this moment exists as well).

In the second test case, the store was closed and opened at the same time — contradiction ("INCORRECT").

考虑第一个测试用例。

一年有 $10$ 个月，一个月有 $10$ 天，一天有 $10$ 秒。

商店在以下 $3$ 个时刻开业：

• 第 $2$ 个月、第 $6$ 天、第 $2$ 秒；
• 第 $4$ 个月、第 $2$ 天、第 $4$ 秒；
• 第 $6$ 个月、第 $4$ 天、第 $6$ 秒。

商店在以下时刻关闭：第 $9$ 个月、第 $9$ 天、第 $9$ 秒。

查询如下：

• 第 $3$ 个月、第 $3$ 天、第 $3$ 秒 —— 营业中（"OPEN"）（因为商店最晚在第 $2$ 个月、第 $2$ 天、第 $2$ 秒已开业，且最早在第 $6$ 个月、第 $6$ 天、第 $6$ 秒才关闭）；
• 第 $10$ 个月、第 $10$ 天、第 $10$ 秒 —— 已关闭（"CLOSED"）（因为在第 $9$ 个月、第 $9$ 天、第 $9$ 秒时商店已关闭）；
• 第 $8$ 个月、第 $8$ 天、第 $8$ 秒 —— 未知（"UNKNOWN"）（因为存在一种营业时间安排使得商店在此时刻处于营业状态，也存在另一种安排使得商店在此时刻处于关闭状态）。

在第二个测试用例中，商店在同一时刻既开业又关闭 —— 矛盾（"INCORRECT"）。