E. Cosmic Rays
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

Given an array of integers $$$s_1, s_2, \ldots, s_l$$$, every second, cosmic rays will cause all $$$s_i$$$ such that $$$i=1$$$ or $$$s_i\neq s_{i-1}$$$ to be deleted simultaneously, and the remaining parts will be concatenated together in order to form the new array $$$s_1, s_2, \ldots, s_{l'}$$$.

Define the strength of an array as the number of seconds it takes to become empty.

You are given an array of integers compressed in the form of $$$n$$$ pairs that describe the array left to right. Each pair $$$(a_i,b_i)$$$ represents $$$a_i$$$ copies of $$$b_i$$$, i.e. $$$\underbrace{b_i,b_i,\cdots,b_i}_{a_i\textrm{ times}}$$$.

For each $$$i=1,2,\dots,n$$$, please find the strength of the sequence described by the first $$$i$$$ pairs.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1\le t\le10^4$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1\le n\le3\cdot10^5$$$) — the length of sequence $$$a$$$.

The next $$$n$$$ lines contain two integers each $$$a_i$$$, $$$b_i$$$ ($$$1\le a_i\le10^9,0\le b_i\le n$$$) — the pairs which describe the sequence.

It is guaranteed that the sum of all $$$n$$$ does not exceed $$$3\cdot10^5$$$.

It is guaranteed that for all $$$1\le i<n$$$, $$$b_i\neq b_{i+1}$$$ holds.

Output

For each test case, print one line containing $$$n$$$ integers — the answer for each prefix of pairs.

Example
Input
4
4
2 0
1 1
3 0
5 1
6
4 6
1 3
4 6
4 0
7 6
6 3
7
9 0
7 1
5 0
7 1
9 0
1 1
2 0
10
10 7
4 9
2 2
7 9
2 8
8 5
11 7
15 5
12 7
4 0
Output
2 2 4 5 
4 4 7 7 10 10 
9 9 9 9 9 9 10 
10 10 10 10 10 10 12 15 15 15
Note

In the first test case, for the prefix of length $$$4$$$, the changes will be $$$[0,0,1,0,0,0,1,1,1,1,1]\rightarrow[0,0,0,1,1,1,1]\rightarrow[0,0,1,1,1]\rightarrow[0,1,1]\rightarrow[1]\rightarrow[]$$$, so the array becomes empty after $$$5$$$ seconds.

In the second test case, for the prefix of length $$$4$$$, the changes will be $$$[6,6,6,6,3,6,6,6,6,0,0,0,0]\rightarrow[6,6,6,6,6,6,0,0,0]\rightarrow[6,6,6,6,6,0,0]\rightarrow[6,6,6,6,0]\rightarrow[6,6,6]\rightarrow[6,6]\rightarrow[6]\rightarrow[]$$$, so the array becomes empty after $$$7$$$ seconds.