{"problem":{"name":"Three Traffic Lights","description":{"content":"There are three traffic lights numbered $1, 2, 3$. Traffic Light $i$ eternally repeats the following pattern: green for $g_i$ seconds, red for $r_i$ seconds, green for $g_i$ seconds, red for $r_i$ sec","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc050_e"},"statements":[{"statement_type":"Markdown","content":"There are three traffic lights numbered $1, 2, 3$. Traffic Light $i$ eternally repeats the following pattern: green for $g_i$ seconds, red for $r_i$ seconds, green for $g_i$ seconds, red for $r_i$ seconds, and so on.\nAll three lights have turned green just now. During the next $(g_1 + r_1)(g_2 + r_2)(g_3 + r_3)$ seconds, what is the total duration of the time when all lights are green? Compute the answer modulo $998,244,353$.\n\n## Constraints\n\n*   $1 \\leq g_1, r_1, g_2, r_2, g_3, r_3 \\leq 10^{12}$\n*   All values in the input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$g_1$ $r_1$ $g_2$ $r_2$ $g_3$ $r_3$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc050_e","tags":[],"sample_group":[["1 1 2 1 3 1","8\n\nDuring the next $24$ seconds,\n\n*   Light $1$ is green during time intervals $[0, 1], [2, 3], [4, 5], [6, 7], [8, 9], [10, 11], [12, 13], [14, 15], [16, 17], [18, 19], [20, 21], [22, 23]$.\n*   Light $2$ is green during time intervals $[0, 2], [3, 5], [6, 8], [9, 11], [12, 14], [15, 17], [18, 20], [21, 23]$.\n*   Light $3$ is green during time intervals $[0, 3], [4, 7], [8, 11], [12, 15], [16, 19], [20, 23]$.\n\nThus, all lights are green during time intervals $[0, 1], [4, 5], [6, 7], [10, 11], [12, 13], [16, 17], [18, 19], [22, 23]$.\nThe total duration is $8$ seconds."],["7 3 5 7 11 4","420"],["999999999991 999999999992 999999999993 999999999994 999999999995 999999999996","120938286"]],"created_at":"2026-03-03 11:01:14"}}