Problem Statement

For integers $l$, $r$, and $x$ ($l \leq r$), let us define $dist(l,r,x)$ as follows.

• If $x<l$: $dist(l,r,x)=l-x$
• If $l \leq x \leq r$: $dist(l,r,x)=0$
• If $r<x$: $dist(l,r,x)=x-r$

You are given $N$ pairs of integers, the $i$-th of which is $(L_i,R_i)$. For each $k=1,2,\cdots,N$, solve the following problem.

• Let us choose an integer $x$ freely and compute $\max(dist(L_1,R_1,x),dist(L_2,R_2,x),\cdots,dist(L_k,R_k,x))$. Find the minimum possible value of this.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq L_i \leq R_i \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
L_1 R_1
L_2 R_2
\vdots
L_N R_N

Output

Print the answers for $k=1,2,\cdots,N$ in this order.