Range Query on a Tree II

Write a program which manipulates a weighted rooted tree $T$ with the following operations:

• $add(v,w)$: add $w$ to all edges from the root to node $u$

• $getSum(u)$: report the sum of weights of all edges from the root to node $u$

The given tree $T$ consists of $n$ nodes and every node has a unique ID from $0$ to $n-1$ respectively where ID of the root is $0$. Note that all weights are initialized to zero.

Constraints

• All the inputs are given in integers
• $2 \leq n \leq 100000$
• $c_j < c_{j+1}$ $( 1 \leq j \leq k-1 )$
• $2 \leq q \leq 200000$
• $1 \leq u,v \leq n-1$
• $1 \leq w \leq 10000$

Input

The input is given in the following format.

$n$ $node_0$ $node_1$ $node_2$ $:$ $node_{n-1}$ $q$ $query_1$ $query_2$ $:$ $query_{q}$

The first line of the input includes an integer $n$, the number of nodes in the tree.

In the next $n$ lines,the information of node $i$ is given in the following format:

ki c1 c2 ... ck

$k_i$ is the number of children of node $i$, and $c_1$ $c_2$ ... $c_{k_i}$ are node IDs of 1st, ... $k$th child of node $i$.

In the next line, the number of queries $q$ is given. In the next $q$ lines, $i$th query is given in the following format:

0 v w

or

1 u

The first integer represents the type of queries.'0' denotes $add(v, w)$ and '1' denotes $getSum(u)$.

Output

For each $getSum$ query, print the sum in a line.

Examples

Input

6 2 1 2 2 3 5 0 0 0 1 4 7 1 1 0 3 10 1 2 0 4 20 1 3 0 5 40 1 4

Output

0 0 40 150

Input

4 1 1 1 2 1 3 0 6 0 3 1000 0 2 1000 0 1 1000 1 1 1 2 1 3

Output

3000 5000 6000

inputFormat

inputs are given in integers

• $2 \leq n \leq 100000$
• $c_j < c_{j+1}$ $( 1 \leq j \leq k-1 )$
• $2 \leq q \leq 200000$
• $1 \leq u,v \leq n-1$
• $1 \leq w \leq 10000$

Input

The input is given in the following format.

$n$ $node_0$ $node_1$ $node_2$ $:$ $node_{n-1}$ $q$ $query_1$ $query_2$ $:$ $query_{q}$

The first line of the input includes an integer $n$, the number of nodes in the tree.

In the next $n$ lines,the information of node $i$ is given in the following format:

ki c1 c2 ... ck

$k_i$ is the number of children of node $i$, and $c_1$ $c_2$ ... $c_{k_i}$ are node IDs of 1st, ... $k$th child of node $i$.

In the next line, the number of queries $q$ is given. In the next $q$ lines, $i$th query is given in the following format:

0 v w

or

1 u

The first integer represents the type of queries.'0' denotes $add(v, w)$ and '1' denotes $getSum(u)$.

outputFormat

Output

For each $getSum$ query, print the sum in a line.

Examples

Input

6 2 1 2 2 3 5 0 0 0 1 4 7 1 1 0 3 10 1 2 0 4 20 1 3 0 5 40 1 4

Output

0 0 40 150

Input

4 1 1 1 2 1 3 0 6 0 3 1000 0 2 1000 0 1 1000 1 1 1 2 1 3

Output

3000 5000 6000

样例

4
1 1
1 2
1 3
0
6
0 3 1000
0 2 1000
0 1 1000
1 1
1 2
1 3

3000
5000
6000

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