There is an online game with $N$ registered players.  
Today, which is the $10^{100}$-th day since its launch, the developer Takahashi examined the users' login history. It turned out that the $i$-th player logged in for $B_i$ consecutive days from Day $A_i$, where Day $1$ is the launch day, and did not log in for the other days. In other words, the $i$-th player logged in on Day $A_i$, $A_i+1$, $\ldots$, $A_i+B_i-1$, and only on those days.  
For each integer $k$ such that $1\leq k\leq N$, find the number of days on which exactly $k$ players logged in.

Input is given from Standard Input in the following format:

```
$N$
$A_1$ $B_1$
$A_2$ $B_2$
$:$
$A_N$ $B_N$
```

Print $N$ integers with spaces in between, as follows:

```
$D_1$ $D_2$ $\cdots$ $D_N$
```

Here, $D_i$ denotes the number of days on which exactly $k$ players logged in.

-   $1 \leq N \leq 2\times 10^5$
-   $1 \leq A_i \leq 10^9$
-   $1 \leq B_i \leq 10^9$
-   All values in input are integers.

2 2 0

The first player logged in on Day 1, 2, the second player logged in on Day 2, 3, 4, and the third player logged in on Day 3 only.

Thus, we can see that Day 1, 4 had 1 player logged in, Day 2, 3 had 2 players logged in, and the other days had no players logged in.

The answer is: there were 2 days with exactly 1 player logged in, 2 days with exactly 2 players logged in, and 0 days with exactly 3 players logged in.

0 1000000000

There may be two or more players who logged in during the same period.