CF1175B.Catch Overflow!

普及/提高-

通过率:0%

时间限制:1.00s

内存限制:256MB

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题目描述

You are given a function ff written in some basic language. The function accepts an integer value, which is immediately written into some variable xx. xx is an integer variable and can be assigned values from 00 to 232−12^{32}-1. The function contains three types of commands:

  • for nn — for loop;
  • end — every command between "for nn" and corresponding "end" is executed nn times;
  • add — adds 1 to xx.

After the execution of these commands, value of xx is returned.

Every "for nn" is matched with "end", thus the function is guaranteed to be valid. "for nn" can be immediately followed by "end"."add" command can be outside of any for loops.

Notice that "add" commands might overflow the value of xx! It means that the value of xx becomes greater than 232−12^{32}-1 after some "add" command.

Now you run f(0)f(0) and wonder if the resulting value of xx is correct or some overflow made it incorrect.

If overflow happened then output "OVERFLOW!!!", otherwise print the resulting value of xx.

你被给定一个用某种基础语言编写的函数 ff。该函数接受一个整数值,该值会立即被写入某个变量 xx 中。xx 是一个整型变量,其取值范围为 00 到 232−12^{32}-1。该函数包含以下三种命令:

  • for $n$ — 表示一个循环;
  • end — 位于对应 for $n$ 和该 end 之间的所有命令将被执行 nn 次;
  • add — 将 xx 的值加 11。

执行完这些命令后,函数返回 xx 的值。

每个 for $n$ 都有唯一匹配的 end,因此该函数保证是合法的。for $n$ 后可直接跟 end。add 命令可以出现在任意 for 循环之外。

注意:add 命令可能导致 xx 溢出!即在某个 add 命令执行后,xx 的值可能超过 232−12^{32}-1。

现在你运行 f(0)f(0),并想知道最终得到的 xx 值是否正确,还是因溢出而变得不正确。

如果发生了溢出,则输出 "OVERFLOW!!!";否则,输出 xx 的最终值。

输入格式

The first line contains a single integer ll (1≤l≤1051 \le l \le 10^5) — the number of lines in the function.

Each of the next ll lines contains a single command of one of three types:

  • for nn (1≤n≤1001 \le n \le 100) — for loop;
  • end — every command between "for nn" and corresponding "end" is executed nn times;
  • add — adds 1 to xx.

第一行包含一个整数 ll(1≤l≤1051 \le l \le 10^5)—— 表示函数中的行数。

接下来的 ll 行中,每行包含一条命令,命令类型为以下三种之一:

  • for $n$(1≤n≤1001 \le n \le 100)—— 表示一个 for 循环;
  • end —— 表示与最近未匹配的 for $n$ 对应的结束;位于 for $n$ 和对应 end 之间的所有命令将被执行 nn 次;
  • add —— 将变量 xx 的值加 1。

输出格式

If overflow happened during execution of f(0)f(0), then output "OVERFLOW!!!", otherwise print the resulting value of xx.

如果在执行 f(0)f(0) 过程中发生溢出,则输出 "OVERFLOW!!!",否则输出 xx 的最终值。

输入输出样例

  • 输入#1

    9
    add
    for 43
    end
    for 10
    for 15
    add
    end
    add
    end

    输出#1

    161
  • 输入#2

    2
    for 62
    end

    输出#2

    0
  • 输入#3

    11
    for 100
    for 100
    for 100
    for 100
    for 100
    add
    end
    end
    end
    end
    end

    输出#3

    OVERFLOW!!!

说明/提示

In the first example the first "add" is executed 1 time, the second "add" is executed 150 times and the last "add" is executed 10 times. Note that "for nn" can be immediately followed by "end" and that "add" can be outside of any for loops.

In the second example there are no commands "add", thus the returning value is 0.

In the third example "add" command is executed too many times, which causes xx to go over 232−12^{32}-1.

在第一个例子中,第一个“add”执行了 1 次,第二个“add”执行了 150 次,最后一个“add”执行了 10 次。注意,“for nn”可以紧跟着“end”,且“add”可以位于任意 for 循环之外。

在第二个例子中,没有“add”命令,因此返回值为 0。

在第三个例子中,“add”命令执行次数过多,导致 xx 超过 232−12^{32}-1。

输入解题思路,AI测评打分。不知道怎么写?

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