Cossack Vus and Time Travel#10704

Cossack Vus and Time Travel

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Cossack Vus invented a time machine.

He has already traveled in time to the $d_{1}$ d_1-th day of the $m_{1}$ m_1-th month of some year. It turned out to be the $w_{1}$ w_1-th day of the week.

Now Cossack Vus plans to travel in time to the $d_{2}$ d_2-th day of the $m_{2}$ m_2-th month of the same year. Help him find out what day of the week it will be.

Assume that this year is not a leap year, so:

the $1$ st month (January) has $31$ days;
the $2$ nd month (February) has $28$ days;
the $3$ rd month (March) has $31$ days;
the $4$ th month (April) has $30$ days;
the $5$ th month (May) has $31$ days;
the $6$ th month (June) has $30$ days;
the $7$ th month (July) has $31$ days;
the $8$ th month (August) has $31$ days;
the $9$ th month (September) has $30$ days;
the $10$ th month (October) has $31$ days;
the $11$ th month (November) has $30$ days;
the $12$ th month (December) has $31$ days.

Input

The first line contains three integers $m_{1}$ m_1, $d_{1}$ d_1 and $w_{1}$ w_1 ( $1 \leq m_{1} \leq 12$ 1 \le m_1 \le 12, $1 \leq d_{1} \leq (number of days in month m_{1})$ 1 \le d_1 \le (\text{number of days in month }m_1), $1 \leq w_{1} \leq 7$ 1 \le w_1 \le 7) — the month, day, and day of the week of the first date.

The second line contains two integers $m_{2}$ m_2 and $d_{2}$ d_2 ( $1 \leq m_{2} \leq 12$ 1 \le m_2 \le 12, $1 \leq d_{2} \leq (number of days in month m_{2})$ 1 \le d_2 \le (\text{number of days in month }m_2)) — the month and day of the second date.

Output

Print one number $w_{2}$ w_2 ( $1 \leq w_{2} \leq 7$ 1 \le w_2 \le 7) — the day of the week of the second date.

Examples

Example 1

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Example 2

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Note

In the first example, Cossack Vus first traveled to August 26 (the $4$ th day of the week, i.e., Thursday), and then to September 13. We can assume this is the year 2021 (in 2021, August 26 is indeed a Thursday). Let's check the calendar for what day of the week September 13 will be. It's Monday (the $1$ st day of the week), so the answer is $1$ .

In the second example, Cossack Vus first traveled to February 1 (Sunday), and then to January 31. This is definitely not 2021. But we know that January 31 comes before February 1. Therefore, the answer is the day of the week before Sunday, which is Saturday.

d_{1}

m_{1}

w_{1}

d_{2}

m_{2}

m_{1}

d_{1}

w_{1}

1 \leq m_{1} \leq 12

1 \leq d_{1} \leq (number of days in month m_{1})

1 \leq w_{1} \leq 7

m_{2}

d_{2}

1 \leq m_{2} \leq 12

1 \leq d_{2} \leq (number of days in month m_{2})

w_{2}

1 \leq w_{2} \leq 7