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Fixed points P34682

Statement

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Let S = x₁, …, x_n be a sequence of integer numbers such that x₁ < … < x_n. For every integer number a and every index 1 ≤ i ≤ n, define f_a(i) = x_i + a. Write a program that, given S and a, tells whether there is some i such that f_a(i) = i.

Input

Input consists of several cases. Every case begins with n, followed by S, followed by a number m, followed by m different integer numbers a₁, …, a_m. Assume 1 ≤ n ≤ 10⁶.

Output

For every case, print its number starting at 1. Afterwards, for every a_j print the position of its fixed point. If no fixed point exists, state so. If there is more than one fixed point, print the smallest one. Print a blank line after the output for every case.

Public test cases

Input

5
-7 -2 0 4 8
1
0

5
0 1 2 3 4
3
0 -1 1

Output

Sequence #1
fixed point for 0: 4

Sequence #2
no fixed point for 0
no fixed point for -1
fixed point for 1: 1

Information

Author: Salvador Roura
Language: English
Official solutions: C++ Python
User solutions: C C++ Python