You are given a radio system consisting of $n$ radios. Each radio $i$ has the following properties:
+ It can receive signals from radios within the range $a_i$ to $b_i$.
+ It can send signals to radios within the range $c_i$ to $d_i$.
+ It takes $t_i$ units of time for the radio to process a signal.
To send a signal from radio $i$ to radio $j$, it costs $t_i + t_j + j - i$ units of time. Your task is to find the minimum unit of time for each radio $2, 3, ..., n$ to receive a signal from radio $1$.
### Input
- First line contains an integer $n$.
- Each line in the next $n$ line contains five integers $t_i,a_i,b_i,c_i,d_i$.
### Output
- Your program should output $n-1$ integers, representing the minimum unit of time for radios $2, 3, ..., n$ to receive a signal from radio $1$. If it is impossible to send receive signal, output `-1` instead.
### Constraints
- $1 \le n \le 10^5$.
- $1 \le a_i \le b_i \le i \le n$.
- $1 \le i \le c_i \le d_i \le n$.
- $1 \le t_i \le 10^9$.
### Example
Input:
```
5
2 1 1 2 4
7 1 1 5 5
1 1 2 4 5
0 2 3 4 5
3 1 4 5 5
```
Output:
```
10 5 7 11
```
