Full Two-Sample T-Test Decision

Fernpost, a courier firm, has been running rival versions of its driver onboarding checklist across different depots. Every new driver is scored out of 100 on route accuracy at the end of week one, and each trial reports, for both cohorts, how many drivers took part, what they averaged, and how spread out their scores were. Operations wants to standardise on one checklist and needs an answer on whether a cohort's lead is more than noise. The first trial put 12 drivers on version A, averaging 75 with a standard deviation of 8, against 15 drivers on version B averaging 70 with a standard deviation of 9.

The rule was fixed before any scores came in: a two-sided test at an agreed significance level, read against the right degrees of freedom for the two cohort sizes. The matching boundary is supplied with each trial — for that first pair, 25 degrees of freedom at 5% gives 2.060.

Task: Print exactly reject or exactly fail to reject, lowercase, on one line. The conventions: independent samples, not paired; equal population variances assumed, so the pooled, equal-variance t-statistic rather than Welch's; the spreads given are sample standard deviations; the test is two-sided, so it is the statistic's distance from zero that is measured against the boundary; and the comparison is strict, so landing exactly on the boundary does not reject.

Input

Seven lines, each holding one number, in this order: cohort A's size, mean and sample standard deviation; then cohort B's size, mean and sample standard deviation; then the boundary. The two sizes are whole numbers of at least 2; the rest are decimals.

Output

One line holding one of the two phrases above, in lower case, and nothing else.

Example:

Input:
12
75
8
15
70
9
2.060

Output:
fail to reject