310799: CF1889D. Game of Stacks

D. Game of Stackstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard output

You have $n$ stacks $r_1,r_2,\ldots,r_n$. Each stack contains some positive integers ranging from $1$ to $n$.

Define the following functions:

function init(pos):
    stacks := an array that contains n stacks r[1], r[2], ..., r[n]
    return get(stacks, pos)

function get(stacks, pos):
    if stacks[pos] is empty:
        return pos
    else:
        new_pos := the top element of stacks[pos]
        pop the top element of stacks[pos]
        return get(stacks, new_pos)

You want to know the values returned by $\texttt{init(1)}, \texttt{init(2)}, \ldots, \texttt{init(n)}$.

Note that, during these calls, the stacks $r_1,r_2,\ldots,r_n$ don't change, so the calls $\texttt{init(1)}, \texttt{init(2)}, \ldots, \texttt{init(n)}$ are independent.

Input

The first line of the input contains one integer $n$ ($1\le n\le 10^5$) — the length of the array $r$.

Each of the following $n$ lines contains several integers. The first integer $k_i$ ($0\le k_i\le 10^5$) represents the number of elements in the $i$-th stack, and the following $k_i$ positive integers $c_{i,1},c_{i,2},\ldots,c_{i,k_i}$ ($1\le c_{i,j}\le n$) represent the elements in the $i$-th stack. $c_{i,1}$ is the bottom element.

In each test, $\sum k_i\le 10^6$.

Output

You need to output $n$ values, the $i$-th of which is the value returned by $\texttt{init(i)}$.

ExamplesInput

3
3 1 2 2
3 3 1 2
3 1 2 1

Output

1 2 2

Input

5
5 1 2 4 3 4
6 1 2 5 3 3 4
6 1 1 4 4 4 2
9 3 1 4 2 3 5 5 1 2
4 4 4 1 3

Output

1 1 1 1 1

Note

In the first example:

• When you call $\texttt{init(1)}$, set $\texttt{stacks := [[1,2,2],[3,1,2],[1,2,1]]}$, and then call $\texttt{get(stacks, 1)}$.
  • $\texttt{stacks[1]}$ is not empty, set $\texttt{new_pos := 2}$, and pop the top element of $\texttt{stacks[1]}$, which makes $\texttt{stacks}$ become $[[1,2],[3,1,2],[1,2,1]]$, and then call $\texttt{get(stacks, 2)}$.
  • $\texttt{stacks[2]}$ is not empty, set $\texttt{new_pos := 2}$, and pop the top element of $\texttt{stacks[2]}$, which makes $\texttt{stacks}$ become $[[1,2],[3,1],[1,2,1]]$, and then call $\texttt{get(stacks, 2)}$.
  • $\texttt{stacks[2]}$ is not empty, set $\texttt{new_pos := 1}$, and pop the top element of $\texttt{stacks[2]}$, which makes $\texttt{stacks}$ become $[[1,2],[3],[1,2,1]]$, and then call $\texttt{get(stacks, 1)}$.
  • $\texttt{stacks[1]}$ is not empty, set $\texttt{new_pos := 2}$, and pop the top element of $\texttt{stacks[1]}$, which makes $\texttt{stacks}$ become $[[1],[3],[1,2,1]]$, and then call $\texttt{get(stacks, 2)}$.
  • $\texttt{stacks[2]}$ is not empty, set $\texttt{new_pos := 3}$, and pop the top element of $\texttt{stacks[2]}$, which makes $\texttt{stacks}$ become $[[1],[],[1,2,1]]$, and then call $\texttt{get(stacks, 3)}$.
  • $\texttt{stacks[3]}$ is not empty, set $\texttt{new_pos := 1}$, and pop the top element of $\texttt{stacks[3]}$, which makes $\texttt{stacks}$ become $[[1],[],[1,2]]$, and then call $\texttt{get(stacks, 1)}$.
  • $\texttt{stacks[1]}$ is not empty, set $\texttt{new_pos := 1}$, and pop the top element of $\texttt{stacks[1]}$, which makes $\texttt{stacks}$ become $[[],[],[1,2]]$, and then call $\texttt{get(stacks, 1)}$.
  • $\texttt{stacks[1]}$ is empty, return $1$.
• When you call $\texttt{init(2)}$, set $\texttt{stacks := [[1,2,2],[3,1,2],[1,2,1]]}$, and then call $\texttt{get(stacks, 2)}$.
  • $\texttt{stacks[2]}$ is not empty, set $\texttt{new_pos := 2}$, and pop the top element of $\texttt{stacks[2]}$, which makes $\texttt{stacks}$ become $[[1,2,2],[3,1],[1,2,1]]$, and then call $\texttt{get(stacks, 2)}$.
  • $\texttt{stacks[2]}$ is not empty, set $\texttt{new_pos := 1}$, and pop the top element of $\texttt{stacks[2]}$, which makes $\texttt{stacks}$ become $[[1,2,2],[3],[1,2,1]]$, and then call $\texttt{get(stacks, 1)}$.
  • $\texttt{stacks[1]}$ is not empty, set $\texttt{new_pos := 2}$, and pop the top element of $\texttt{stacks[1]}$, which makes $\texttt{stacks}$ become $[[1,2],[3],[1,2,1]]$, and then call $\texttt{get(stacks, 2)}$.
  • $\texttt{stacks[2]}$ is not empty, set $\texttt{new_pos := 3}$, and pop the top element of $\texttt{stacks[2]}$, which makes $\texttt{stacks}$ become $[[1,2],[],[1,2,1]]$, and then call $\texttt{get(stacks, 3)}$.
  • $\texttt{stacks[3]}$ is not empty, set $\texttt{new_pos := 1}$, and pop the top element of $\texttt{stacks[3]}$, which makes $\texttt{stacks}$ become $[[1,2],[],[1,2]]$, and then call $\texttt{get(stacks, 1)}$.
  • $\texttt{stacks[1]}$ is not empty, set $\texttt{new_pos := 2}$, and pop the top element of $\texttt{stacks[1]}$, which makes $\texttt{stacks}$ become $[[1],[],[1,2]]$, and then call $\texttt{get(stacks, 2)}$.
  • $\texttt{stacks[2]}$ is empty, return $2$.
• When you call $\texttt{init(3)}$, set $\texttt{stacks := [[1,2,2],[3,1,2],[1,2,1]]}$, and then call $\texttt{get(stacks, 3)}$.
  • $\texttt{stacks[3]}$ is not empty, set $\texttt{new_pos := 1}$, and pop the top element of $\texttt{stacks[3]}$, which makes $\texttt{stacks}$ become $[[1,2,2],[3,1,2],[1,2]]$, and then call $\texttt{get(stacks, 1)}$.
  • $\texttt{stacks[1]}$ is not empty, set $\texttt{new_pos := 2}$, and pop the top element of $\texttt{stacks[1]}$, which makes $\texttt{stacks}$ become $[[1,2],[3,1,2],[1,2]]$, and then call $\texttt{get(stacks, 2)}$.
  • $\texttt{stacks[2]}$ is not empty, set $\texttt{new_pos := 2}$, and pop the top element of $\texttt{stacks[2]}$, which makes $\texttt{stacks}$ become $[[1,2],[3,1],[1,2]]$, and then call $\texttt{get(stacks, 2)}$.
  • $\texttt{stacks[2]}$ is not empty, set $\texttt{new_pos := 1}$, and pop the top element of $\texttt{stacks[2]}$, which makes $\texttt{stacks}$ become $[[1,2],[3],[1,2]]$, and then call $\texttt{get(stacks, 1)}$.
  • $\texttt{stacks[1]}$ is not empty, set $\texttt{new_pos := 2}$, and pop the top element of $\texttt{stacks[1]}$, which makes $\texttt{stacks}$ become $[[1],[3],[1,2]]$, and then call $\texttt{get(stacks, 2)}$.
  • $\texttt{stacks[2]}$ is not empty, set $\texttt{new_pos := 3}$, and pop the top element of $\texttt{stacks[2]}$, which makes $\texttt{stacks}$ become $[[1],[],[1,2]]$, and then call $\texttt{get(stacks, 3)}$.
  • $\texttt{stacks[3]}$ is not empty, set $\texttt{new_pos := 2}$, and pop the top element of $\texttt{stacks[3]}$, which makes $\texttt{stacks}$ become $[[1],[],[1]]$, and then call $\texttt{get(stacks, 2)}$.
  • $\texttt{stacks[2]}$ is empty, return $2$.

题目大意：有n个栈，每个栈包含一些从1到n的正整数。定义两个函数，`init(pos)`函数返回`get(stacks, pos)`的值，`get(stacks, pos)`函数从`stacks[pos]`中取出一个元素（如果有的话），然后递归调用`get(stacks, new_pos)`，其中`new_pos`是该元素的值，直到`stacks[pos]`为空，此时返回`pos`。需要求出`init(1)`，`init(2)`，...，`init(n)`的返回值。

输入输出数据格式：
- 输入：
- 第一行包含一个整数n（1≤n≤10^5），表示数组r的长度。
- 接下来的n行，每行包含一些整数。第一个整数k_i（0≤k_i≤10^5）表示第i个栈的元素个数，接下来的k_i个正整数c_{i,1},c_{i,2},...,c_{i,k_i}（1≤c_{i,j}≤n）表示第i个栈的元素。c_{i,1}是栈底元素。
- 每个测试用例中，∑k_i≤10^6。
- 输出：
- 输出n个值，第i个值是`init(i)`的返回值。

示例：
```
输入：
3
3 1 2 2
3 3 1 2
3 1 2 1
输出：
1 2 2
```

```
输入：
5
5 1 2 4 3 4
6 1 2 5 3 3 4
6 1 1 4 4 4 2
9 3 1 4 2 3 5 5 1 2
4 4 4 1 3
输出：
1 1 1 1 1
```题目大意：有n个栈，每个栈包含一些从1到n的正整数。定义两个函数，`init(pos)`函数返回`get(stacks, pos)`的值，`get(stacks, pos)`函数从`stacks[pos]`中取出一个元素（如果有的话），然后递归调用`get(stacks, new_pos)`，其中`new_pos`是该元素的值，直到`stacks[pos]`为空，此时返回`pos`。需要求出`init(1)`，`init(2)`，...，`init(n)`的返回值。 输入输出数据格式： - 输入： - 第一行包含一个整数n（1≤n≤10^5），表示数组r的长度。 - 接下来的n行，每行包含一些整数。第一个整数k_i（0≤k_i≤10^5）表示第i个栈的元素个数，接下来的k_i个正整数c_{i,1},c_{i,2},...,c_{i,k_i}（1≤c_{i,j}≤n）表示第i个栈的元素。c_{i,1}是栈底元素。 - 每个测试用例中，∑k_i≤10^6。 - 输出： - 输出n个值，第i个值是`init(i)`的返回值。 示例： ``` 输入： 3 3 1 2 2 3 3 1 2 3 1 2 1 输出： 1 2 2 ``` ``` 输入： 5 5 1 2 4 3 4 6 1 2 5 3 3 4 6 1 1 4 4 4 2 9 3 1 4 2 3 5 5 1 2 4 4 4 1 3 输出： 1 1 1 1 1 ```