1501_A. Alexey and Train
Alexey is travelling on a train. Unfortunately, due to the bad weather, the train moves slower that it should!

Alexey took the train at the railroad terminal. Let's say that the train starts from the terminal at the moment 0. Also, let's say that the train will visit n stations numbered from 1 to n along its way, and that Alexey destination is the station n.

Alexey learned from the train schedule n integer pairs (a_i, b_i) where a_i is the expected time of train's arrival at the i-th station and b_i is the expected time of departure.

Also, using all information he has, Alexey was able to calculate n integers tm_1, tm_2, ..., tm_n where tm_i is the extra time the train need to travel from the station i - 1 to the station i. Formally, the train needs exactly a_i - b_{i-1} + tm_i time to travel from station i - 1 to station i (if i = 1 then b_0 is the moment the train leave the terminal, and it's equal to 0).

The train leaves the station i, if both conditions are met: 

  1. it's on the station for at least \left⌈ (b_i - a_i)/(2) \right⌉ units of time (division with ceiling); 
  2. current time ≥ b_i. 



Since Alexey spent all his energy on prediction of time delays, help him to calculate the time of arrival at the station n.

Input

The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases.

The first line of each test case contains the single integer n (1 ≤ n ≤ 100) — the number of stations.

Next n lines contain two integers each: a_i and b_i (1 ≤ a_i < b_i ≤ 10^6). It's guaranteed that b_i < a_{i+1}. 

Next line contains n integers tm_1, tm_2, ..., tm_n (0 ≤ tm_i ≤ 10^6).

Output

For each test case, print one integer — the time of Alexey's arrival at the last station.

Example

Input


2
2
2 4
10 12
0 2
5
1 4
7 8
9 10
13 15
19 20
1 2 3 4 5


Output


12
32

Note

In the first test case, Alexey arrives at station 1 without any delay at the moment a_1 = 2 (since tm_1 = 0). After that, he departs at moment b_1 = 4. Finally, he arrives at station 2 with tm_2 = 2 extra time, or at the moment 12.

In the second test case, Alexey arrives at the first station with tm_1 = 1 extra time, or at moment 2. The train, from one side, should stay at the station at least \left⌈ (b_1 - a_1)/(2) \right⌉ = 2 units of time and from the other side should depart not earlier than at moment b_1 = 4. As a result, the trains departs right at the moment 4.

Using the same logic, we can figure out that the train arrives at the second station at the moment 9 and departs at the moment 10; at the third station: arrives at 14 and departs at 15; at the fourth: arrives at 22 and departs at 23. And, finally, arrives at the fifth station at 32.
```python
import sys,os,io
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

for _ in range (int(input())):
    n = int(input())
    a = []
    b = []
    for i in range (n):
        ai,bi =[int(i) for i in input().split()]
        a.append(ai)
        b.append(bi)
    t = [int(i) for i in input().split()]
    d = 0
    curr = 0
    arr = [0 for i in range (n)]
    for i in range (n):
        arr[i] = d + a[i]+t[i]
        diff = (b[i]-a[i])
        if diff%2==0:
            diff = diff//2
        else:
            diff = diff//2 + 1
        leave = max(diff+arr[i], b[i])
        d = leave - b[i]
    print(arr[-1])
        
```