Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Printer

time limit per test

4 secondsmemory limit per test

256 megabytesinput

input.txtoutput

output.txtLet's consider a network printer that functions like that. It starts working at time 0. In each second it can print one page of a text. At some moments of time the printer receives printing tasks. We know that a printer received *n* tasks. Let's number the tasks by consecutive integers from 1 to *n*. Then the task number *i* is characterised by three integers: *t*_{i} is the time when the task came, *s*_{i} is the task's volume (in pages) and *p*_{i} is the task's priority. The priorities of all tasks are distinct.

When the printer receives a task, the task goes to the queue and remains there until all pages from this task are printed. The printer chooses a page to print each time when it either stops printing some page or when it is free and receives a new task. Among all tasks that are in the queue at this moment, the printer chooses the task with the highest priority and next second prints an unprinted page from this task. You can assume that a task goes to the queue immediately, that's why if a task has just arrived by time *t*, the printer can already choose it for printing.

You are given full information about all tasks except for one: you don't know this task's priority. However, we know the time when the last page from this task was finished printing. Given this information, find the unknown priority value and determine the moments of time when the printer finished printing each task.

Input

The first line contains integer *n* (1 ≤ *n* ≤ 50000). Next *n* lines describe the tasks. The *i*-th of these lines contains three integers *t*_{i}, *s*_{i} and *p*_{i}, separated by single spaces (0 ≤ *t*_{i} ≤ 10^{9}, 1 ≤ *s*_{i}, *p*_{i} ≤ 10^{9}). Exactly one task (let's assume that his number is *x*) has number -1 written instead of the priority. All priorities are different. The last line contains integer *T* — the time when the printer finished printing the last page of task *x* (1 ≤ *T* ≤ 10^{15}). Numbers *t*_{i} are not necessarily distinct. The tasks in the input are written in the arbitrary order.

Output

In the first line print integer *p*_{x} — the priority of the task number *x* (1 ≤ *p*_{x} ≤ 10^{9}, remember that all priorities should be distinct). Then print *n* integers, the *i*-th of them represents the moment of time when the last page of the task number *i* finished printing.

It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.

Examples

Input

3

4 3 -1

0 2 2

1 3 3

7

Output

4

7 8 4

Input

3

3 1 2

2 3 3

3 1 -1

4

Output

4

7 6 4

Note

Let's consider the first test case. Let's assume that the unknown priority equals 4, then the printer's actions for each second are as follows:

- the beginning of the 1-st second (time 0). The queue has task 2. The printer prints the first page of this task;
- the beginning of the 2-nd second (time 1). The queue has tasks 2 and 3. The printer prints the first page of task 3;
- the beginning of the 3-rd second (time 2). The queue has tasks 2 and 3. The printer prints the second page of task 3;
- the beginning of the 4-th second (time 3). The queue has tasks 2 and 3. The printer prints the third (last) page of task 3. Thus, by the end of the 4-th second this task will have been printed;
- the beginning of the 5-th second (time 4). The queue has tasks 2 and 1. The printer prints the first page of task 1;
- the beginning of the 6-th second (time 5). The queue has tasks 2 and 1. The printer prints the second page of task 1;
- the beginning of the 7-th second (time 6). The queue has tasks 2 and 1. The printer prints the third (last) page of task 1. Thus, by the end of the 7-th second this task will have been printed;
- the beginning of the 8-th second (time 7). The queue has task 2. The printer prints the second (last) page of task 2. Thus, by the end of the 8-th second this task will have been printed.

In the end, task number 1 will have been printed by the end of the 7-th second, as was required. And tasks 2 and 3 are printed by the end of the of the 8-th and the 4-th second correspondingly.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/15/2019 18:21:18 (e1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|