Problem Statement

E869120 knows the precipitation data for $N$ hours in yuki City.
Initially, the precipitation in hour $i$ ($1 \leq i \leq N$) (the period between $i-1$ hours and $i$ hours after the start of the data) was $A_i$ millimeters.

He tried to calculate the maximum precipitation over $24$ consecutive hours within the $N$ hours of data.

However, as the analysis of the data progresses, the data is changed $Q$ times.

• In the $j$-th change ($1 \leq j \leq Q$), the precipitation in hour $T_j$ is changed to $V_j$ millimeters.
• However, no change to the data ever decreases the precipitation in that hour.

Output

All input data satisfy the following constraints.

• $N$ is an integer between $24$ and $200 \ 000$, inclusive
• $Q$ is an integer between $1$ and $200 \ 000$, inclusive
• $T_j$ is an integer between $1$ and $N$, inclusive
• $A_i$ is an integer between $0$ and $153$, inclusive
• $V_j$ is an integer between $0$ and $153$, inclusive
• No change decreases the precipitation

Input

$N$
$A_1$ $A_2$ $A_3$ ... $A_N$
$Q$
$T_1$ $V_1$
$T_2$ $V_2$
$T_3$ $V_3$
...
$T_Q$ $V_Q$

Output

Output $Q$ lines.
On line $i$, output the maximum precipitation over $24$ consecutive hours immediately after the $i$-th change.

Sample

25
0 0 0 0 2 3 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 2 5 13
2
1 0
1 80

27
94

24
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
24
1 153
2 153
3 153
4 153
5 153
6 153
7 153
8 153
9 153
10 153
11 153
12 153
13 153
14 153
15 153
16 153
17 153
18 153
19 153
20 153
21 153
22 153
23 153
24 153

452
603
753
902
1050
1197
1343
1488
1632
1775
1917
2058
2198
2337
2475
2612
2748
2883
3017
3150
3282
3413
3543
3672

30
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10
5 0
8 0
11 0
3 0
24 0
25 0
16 0
17 0
4 0
19 0

0
0
0
0
0
0
0
0
0
0