Mike has a frog and a flower. His frog is named Xaniar and his flower is named Abol. Initially(at time 0), height of Xaniar is *h*<sub class="lower-index">1</sub> and height of Abol is *h*<sub class="lower-index">2</sub>. Each second, Mike waters Abol and Xaniar.

So, if height of Xaniar is *h*<sub class="lower-index">1</sub> and height of Abol is *h*<sub class="lower-index">2</sub>, after one second height of Xaniar will become <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/2fe18334e8025eeb03e58258a1a73999e06eaded.png" style="max-width: 100.0%;max-height: 100.0%;"/> and height of Abol will become <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/fc063cc983b60502463ef52c01f1c9f44150fd93.png" style="max-width: 100.0%;max-height: 100.0%;"/> where *x*<sub class="lower-index">1</sub>, *y*<sub class="lower-index">1</sub>, *x*<sub class="lower-index">2</sub> and *y*<sub class="lower-index">2</sub> are some integer numbers and <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/57fc4a50a6c33bac9327d8c392910a6dbf5c89bb.png" style="max-width: 100.0%;max-height: 100.0%;"/> denotes the remainder of *a* modulo *b*.

Mike is a competitive programmer fan. He wants to know the minimum time it takes until height of Xania is *a*<sub class="lower-index">1</sub> and height of Abol is *a*<sub class="lower-index">2</sub>.

Mike has asked you for your help. Calculate the minimum time or say it will never happen.
The first line of input contains integer *m* (2 ≤ *m* ≤ 10<sup class="upper-index">6</sup>).

The second line of input contains integers *h*<sub class="lower-index">1</sub> and *a*<sub class="lower-index">1</sub> (0 ≤ *h*<sub class="lower-index">1</sub>, *a*<sub class="lower-index">1</sub> &lt; *m*).

The third line of input contains integers *x*<sub class="lower-index">1</sub> and *y*<sub class="lower-index">1</sub> (0 ≤ *x*<sub class="lower-index">1</sub>, *y*<sub class="lower-index">1</sub> &lt; *m*).

The fourth line of input contains integers *h*<sub class="lower-index">2</sub> and *a*<sub class="lower-index">2</sub> (0 ≤ *h*<sub class="lower-index">2</sub>, *a*<sub class="lower-index">2</sub> &lt; *m*).

The fifth line of input contains integers *x*<sub class="lower-index">2</sub> and *y*<sub class="lower-index">2</sub> (0 ≤ *x*<sub class="lower-index">2</sub>, *y*<sub class="lower-index">2</sub> &lt; *m*).

It is guaranteed that *h*<sub class="lower-index">1</sub> ≠ *a*<sub class="lower-index">1</sub> and *h*<sub class="lower-index">2</sub> ≠ *a*<sub class="lower-index">2</sub>.
def main():
    m, tt = int(input()), [0] * 4
    for i in 0, 2:
        h, a = map(int, input().split())
        x, y = map(int, input().split())
        ha = (h, a)
        for t in range(1, m * 2):
            h = (h * x + y) % m
            if h in ha:
                if h == ha[0]:
                    if tt[i]:
                        tt[i] = t - tt[i]
                        break
                    else:
                        tt[i] = t
                else:
                    if tt[i + 1]:
                        tt[i] = t - tt[i + 1]
                        break
                    else:
                        tt[i + 1] = t
        if not (tt[i] or tt[i + 1]):
            print(-1)
            return
    step1, shift1, step2, shift2 = tt if tt[0] > tt[2] else tt[2:] + tt[:2]
    if step2 == 1:
        print(shift1 if shift1 >= shift2 else shift2 + (shift2 - shift1) % step1)
        return
    for t in range(shift1 - shift2, shift1 - shift2 + step1 * step2, step1):
        if not t % step2:
            print(t + shift2)
            return
    print(-1)


if __name__ == '__main__':
    main()
