Statements of Operations - USD ($)	12 Months Ended
	Dec. 31, 2016		Dec. 31, 2015		Dec. 31, 2014
Investment Income
Interest	$ 9,133,928	[1]	$ 1,546,729	[2]	$ 1,151,784
Expenses
Management fee	34,712,239	[1]	35,055,606	[2]	27,669,705
Brokerage commissions and fees	7,438,871	[1]	6,480,284	[2]	4,580,430
Offering costs			59,479	[2]	16,401
Limitation by Sponsor			(11,814)	[2]	(9,474)
Total expenses	42,151,110	[1]	41,583,555	[2]	32,257,062
Net investment income (loss)	(33,017,182)	[1]	(40,036,826)	[2]	(31,105,278)
Net realized gain (loss) on
Foreign currency forward contracts	(47,075,744)	[1]	138,005,915	[2]	210,564,249
Short-term U.S. government and agency obligations	(15,768)	[1]	47,732	[2]	123,212
Net realized gain (loss)	(1,320,602,359)	[1]	(1,164,531,561)	[2]	(160,550,428)
Change in net unrealized appreciation/depreciation on
Futures contracts	(22,030,613)	[1]	40,193,356	[2]	9,175,329
Foreign currency forward contracts	73,731,339	[1]	(56,805,160)	[2]	(514,227)
Short-term U.S. government and agency obligations	4,832	[1]	(46,135)	[2]	(73,469)
Change in net unrealized appreciation/depreciation	157,868,764	[1]	(39,700,049)	[2]	(46,083,005)
Net realized and unrealized gain (loss)	(1,162,733,595)	[1]	(1,204,231,610)	[2]	(206,633,433)
Net income (loss)	(1,195,750,777)	[1]	(1,244,268,436)	[2]	(237,738,711)
Futures Contracts [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	(1,286,470,453)	[1]	(675,706,798)	[2]	(136,360,050)
Swap Agreements [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	(25,398,375)	[1]	(553,434,721)	[2]	(79,470,613)
Change in net unrealized appreciation/depreciation on
Unrealized gain (loss) on derivatives	108,928,215	[1]	(16,849,426)	[2]	(48,539,505)
Forward Agreements [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	38,357,981	[1]	(73,443,689)	[2]	(155,407,226)
Change in net unrealized appreciation/depreciation on
Unrealized gain (loss) on derivatives	(2,765,009)	[1]	(6,192,684)	[2]	(6,131,133)
ProShares VIX Short-Term Futures ETF [Member]
Investment Income
Interest	466,392		42,319		47,562
Expenses
Management fee	1,632,880		1,062,171		1,083,189
Brokerage commissions and fees	270,159		130,942		82,921
Total expenses	1,903,039		1,193,113		1,166,110
Net investment income (loss)	(1,436,647)		(1,150,794)		(1,118,548)
Net realized gain (loss) on
Short-term U.S. government and agency obligations	6,650		1,703		12,242
Net realized gain (loss)	(195,469,141)		(19,406,840)		(682,105)
Change in net unrealized appreciation/depreciation on
Futures contracts	609,973		(7,343,245)		22,917,306
Short-term U.S. government and agency obligations	3,010		(3,657)		(6,229)
Change in net unrealized appreciation/depreciation	612,983		(7,346,902)		22,911,077
Net realized and unrealized gain (loss)	(194,856,158)		(26,753,742)		22,228,972
Net income (loss)	(196,292,805)		(27,904,536)		21,110,424
ProShares VIX Short-Term Futures ETF [Member] | Futures Contracts [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	(195,475,791)		(19,408,543)		(694,347)
ProShares VIX Mid-Term Futures ETF [Member]
Investment Income
Interest	107,409		8,293		16,573
Expenses
Management fee	369,016		233,390		392,120
Brokerage commissions and fees	32,884		15,503		10,931
Total expenses	401,900		248,893		403,051
Net investment income (loss)	(294,491)		(240,600)		(386,478)
Net realized gain (loss) on
Short-term U.S. government and agency obligations	499		1,355		1,742
Net realized gain (loss)	(11,085,007)		(3,334,581)		(14,377,068)
Change in net unrealized appreciation/depreciation on
Futures contracts	(943,885)		(605,025)		5,157,354
Short-term U.S. government and agency obligations	(1,079)		(327)		187
Change in net unrealized appreciation/depreciation	(944,964)		(605,352)		5,157,541
Net realized and unrealized gain (loss)	(12,029,971)		(3,939,933)		(9,219,527)
Net income (loss)	(12,324,462)		(4,180,533)		(9,606,005)
ProShares VIX Mid-Term Futures ETF [Member] | Futures Contracts [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	(11,085,506)		(3,335,936)		(14,378,810)
ProShares Short VIX Short-Term Futures ETF [Member]
Investment Income
Interest	1,126,057		180,686		81,544
Expenses
Management fee	4,448,808		4,043,491		2,785,597
Brokerage commissions and fees	2,074,099		1,935,395		1,581,416
Total expenses	6,522,907		5,978,886		4,367,013
Net investment income (loss)	(5,396,850)		(5,798,200)		(4,285,469)
Net realized gain (loss) on
Short-term U.S. government and agency obligations	(11,670)		35,629		19,363
Net realized gain (loss)	440,379,719		69,828,657		76,945,361
Change in net unrealized appreciation/depreciation on
Futures contracts	(21,056,026)		27,098,564		(24,469,104)
Short-term U.S. government and agency obligations	(6,824)		8,936		(1,764)
Change in net unrealized appreciation/depreciation	(21,062,850)		27,107,500		(24,470,868)
Net realized and unrealized gain (loss)	419,316,869		96,936,157		52,474,493
Net income (loss)	413,920,019		91,137,957		48,189,024
ProShares Short VIX Short-Term Futures ETF [Member] | Futures Contracts [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	440,391,389		69,793,028		76,925,998
ProShares Ultra VIX Short-Term Futures ETF [Member]
Investment Income
Interest	1,639,964		156,187		72,700
Expenses
Management fee	6,417,822		4,362,460		2,868,337
Brokerage commissions and fees	4,158,919		3,203,875		2,563,849
Total expenses	10,576,741		7,566,335		5,432,186
Net investment income (loss)	(8,936,777)		(7,410,148)		(5,359,486)
Net realized gain (loss) on
Short-term U.S. government and agency obligations	15,949		(49,718)		9,921
Net realized gain (loss)	(1,567,324,739)		(392,223,946)		(139,402,604)
Change in net unrealized appreciation/depreciation on
Futures contracts	(19,866,703)		(27,690,787)		63,595,164
Short-term U.S. government and agency obligations	(28,844)		26,647		(4,701)
Change in net unrealized appreciation/depreciation	(19,895,547)		(27,664,140)		63,590,463
Net realized and unrealized gain (loss)	(1,587,220,286)		(419,888,086)		(75,812,141)
Net income (loss)	(1,596,157,063)		(427,298,234)		(81,171,627)
ProShares Ultra VIX Short-Term Futures ETF [Member] | Futures Contracts [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	(1,567,340,688)		(392,174,228)		(139,412,525)
ProShares UltraShort Bloomberg Crude Oil [Member]
Investment Income
Interest	500,160		60,884		110,620
Expenses
Management fee	1,755,696		1,978,613		2,448,428
Brokerage commissions and fees	153,428		248,482		78,033
Total expenses	1,909,124		2,227,095		2,526,461
Net investment income (loss)	(1,408,964)		(2,166,211)		(2,415,841)
Net realized gain (loss) on
Short-term U.S. government and agency obligations	(4,064)		14,458		20,701
Net realized gain (loss)	(67,756,228)		91,684,782		99,347,798
Change in net unrealized appreciation/depreciation on
Futures contracts	(3,891,328)		(13,342,090)		17,039,376
Short-term U.S. government and agency obligations	1,712		(4,396)		(8,704)
Change in net unrealized appreciation/depreciation	(22,509,153)		(33,951,907)		46,381,649
Net realized and unrealized gain (loss)	(90,265,381)		57,732,875		145,729,447
Net income (loss)	(91,674,345)		55,566,664		143,313,606
ProShares UltraShort Bloomberg Crude Oil [Member] | Futures Contracts [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	(12,045,454)		46,904,474		44,472,509
ProShares UltraShort Bloomberg Crude Oil [Member] | Swap Agreements [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	(55,706,710)		44,765,850		54,854,588
Change in net unrealized appreciation/depreciation on
Unrealized gain (loss) on derivatives	(18,619,537)		(20,605,421)		29,350,977
ProShares UltraShort Bloomberg Natural Gas [Member]
Investment Income
Interest	19,053		5,830		16,306
Expenses
Management fee	81,259		112,277		385,014
Brokerage commissions and fees	59,966		70,677		92,199
Total expenses	141,225		182,954		477,213
Net investment income (loss)	(122,172)		(177,124)		(460,907)
Net realized gain (loss) on
Short-term U.S. government and agency obligations	3,139		29		5,163
Net realized gain (loss)	589,999		15,212,833		8,796,882
Change in net unrealized appreciation/depreciation on
Futures contracts	1,989,133		(6,412,629)		2,899,165
Short-term U.S. government and agency obligations	(388)		168		72
Change in net unrealized appreciation/depreciation	1,988,745		(6,412,461)		2,899,237
Net realized and unrealized gain (loss)	2,578,744		8,800,372		11,696,119
Net income (loss)	2,456,572		8,623,248		11,235,212
ProShares UltraShort Bloomberg Natural Gas [Member] | Futures Contracts [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	586,860		15,212,804		8,791,719
ProShares UltraShort Gold [Member]
Investment Income
Interest	164,570		31,999		40,675
Expenses
Management fee	625,950		735,540		898,453
Brokerage commissions and fees	43		41		39
Total expenses	625,993		735,581		898,492
Net investment income (loss)	(461,423)		(703,582)		(857,817)
Net realized gain (loss) on
Short-term U.S. government and agency obligations	(378)		1,301		3,873
Net realized gain (loss)	(12,241,129)		12,708,936		(5,312,609)
Change in net unrealized appreciation/depreciation on
Futures contracts	13,760		9,740		(19,040)
Short-term U.S. government and agency obligations	2,028		(2,950)		868
Change in net unrealized appreciation/depreciation	1,240,412		4,098,510		(7,934,003)
Net realized and unrealized gain (loss)	(11,000,717)		16,807,446		(13,246,612)
Net income (loss)	(11,462,140)		16,103,864		(14,104,429)
ProShares UltraShort Gold [Member] | Futures Contracts [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	(29,440)		15,950		23,310
ProShares UltraShort Gold [Member] | Forward Agreements [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	(12,211,311)		12,691,685		(5,339,792)
Change in net unrealized appreciation/depreciation on
Unrealized gain (loss) on derivatives	1,224,624		4,091,720		(7,915,831)
ProShares UltraShort Silver [Member]
Investment Income
Interest	93,483		23,831		30,901
Expenses
Management fee	349,293		540,253		616,703
Brokerage commissions and fees	43		42		39
Total expenses	349,336		540,295		616,742
Net investment income (loss)	(255,853)		(516,464)		(585,841)
Net realized gain (loss) on
Short-term U.S. government and agency obligations	(1,916)		(2,787)		4,234
Net realized gain (loss)	(17,556,630)		10,756,758		15,119,117
Change in net unrealized appreciation/depreciation on
Futures contracts	21,340		4,410		(12,640)
Short-term U.S. government and agency obligations	367		(794)		(2,414)
Change in net unrealized appreciation/depreciation	(3,372,326)		4,186,942		2,807,756
Net realized and unrealized gain (loss)	(20,928,956)		14,943,700		17,926,873
Net income (loss)	(21,184,809)		14,427,236		17,341,032
ProShares UltraShort Silver [Member] | Futures Contracts [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	(40,250)		15,575		32,275
ProShares UltraShort Silver [Member] | Forward Agreements [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	(17,514,464)		10,743,970		15,082,608
Change in net unrealized appreciation/depreciation on
Unrealized gain (loss) on derivatives	(3,394,033)		4,183,326		2,822,810
ProShares Short Euro [Member]
Investment Income
Interest	32,959		4,504		4,716
Expenses
Management fee	153,021		179,286		121,126
Brokerage commissions and fees	2,666		3,979		1,837
Total expenses	155,687		183,265		122,963
Net investment income (loss)	(122,728)		(178,761)		(118,247)
Net realized gain (loss) on
Short-term U.S. government and agency obligations	33		218		402
Net realized gain (loss)	663,807		1,559,643		1,593,450
Change in net unrealized appreciation/depreciation on
Futures contracts	(110,538)		(141,893)		418,562
Short-term U.S. government and agency obligations	12		(170)		(472)
Change in net unrealized appreciation/depreciation	(110,526)		(142,063)		418,090
Net realized and unrealized gain (loss)	553,281		1,417,580		2,011,540
Net income (loss)	430,553		1,238,819		1,893,293
ProShares Short Euro [Member] | Futures Contracts [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	663,774		1,559,425		1,593,048
ProShares UltraShort Australian Dollar [Member]
Investment Income
Interest	43,459		5,998		8,225
Expenses
Management fee	175,191		199,845		208,597
Brokerage commissions and fees	13,920		16,140		12,811
Total expenses	189,111		215,985		221,408
Net investment income (loss)	(145,652)		(209,987)		(213,183)
Net realized gain (loss) on
Short-term U.S. government and agency obligations	495		225		492
Net realized gain (loss)	(2,786,709)		4,330,688		2,296,708
Change in net unrealized appreciation/depreciation on
Futures contracts	1,602,610		(1,163,751)		(174,124)
Short-term U.S. government and agency obligations	279		(553)		(1,463)
Change in net unrealized appreciation/depreciation	1,602,889		(1,164,304)		(175,587)
Net realized and unrealized gain (loss)	(1,183,820)		3,166,384		2,121,121
Net income (loss)	(1,329,472)		2,956,397		1,907,938
ProShares UltraShort Australian Dollar [Member] | Futures Contracts [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	(2,787,204)		4,330,463		2,296,216
ProShares UltraShort Euro [Member]
Investment Income
Interest	1,012,886		264,845		199,596
Expenses
Management fee	3,777,543		5,265,432		4,193,741
Total expenses	3,777,543		5,265,432		4,193,741
Net investment income (loss)	(2,764,657)		(5,000,587)		(3,994,145)
Net realized gain (loss) on
Foreign currency forward contracts	(25,711,518)		131,651,572		83,678,955
Short-term U.S. government and agency obligations	242		22,509		4,637
Net realized gain (loss)	(25,711,276)		131,674,081		83,683,592
Change in net unrealized appreciation/depreciation on
Foreign currency forward contracts	44,873,267		(45,473,330)		30,511,501
Short-term U.S. government and agency obligations	12,675		(23,782)		(12,286)
Change in net unrealized appreciation/depreciation	44,885,942		(45,497,112)		30,499,215
Net realized and unrealized gain (loss)	19,174,666		86,176,969		114,182,807
Net income (loss)	16,410,009		81,176,382		110,188,662
ProShares UltraShort Yen [Member]
Investment Income
Interest	531,771		135,814		197,253
Expenses
Management fee	2,141,333		3,759,492		3,938,854
Total expenses	2,141,333		3,759,492		3,938,854
Net investment income (loss)	(1,609,562)		(3,623,678)		(3,741,601)
Net realized gain (loss) on
Foreign currency forward contracts	(22,220,271)		8,809,464		127,846,225
Short-term U.S. government and agency obligations	(5,910)		(3,035)		13,833
Net realized gain (loss)	(22,226,181)		8,806,429		127,860,058
Change in net unrealized appreciation/depreciation on
Foreign currency forward contracts	30,640,389		(12,316,677)		(30,965,459)
Short-term U.S. government and agency obligations	16,827		(30,886)		(20,893)
Change in net unrealized appreciation/depreciation	30,657,216		(12,347,563)		(30,986,352)
Net realized and unrealized gain (loss)	8,431,035		(3,541,134)		96,873,706
Net income (loss)	6,821,473		(7,164,812)		93,132,105
ProShares Ultra Bloomberg Crude Oil [Member]
Investment Income
Interest	2,170,633		396,158		68,292
Expenses
Management fee	8,263,078		8,230,180		1,769,248
Brokerage commissions and fees	538,935		639,133		65,408
Total expenses	8,802,013		8,869,313		1,834,656
Net investment income (loss)	(6,631,380)		(8,473,155)		(1,766,364)
Net realized gain (loss) on
Short-term U.S. government and agency obligations	(17,374)		22,728		11,806
Net realized gain (loss)	74,043,666		(896,154,368)		(243,314,151)
Change in net unrealized appreciation/depreciation on
Futures contracts	23,466,479		28,545,473		(47,101,448)
Short-term U.S. government and agency obligations	5,463		(6,857)		(7,333)
Change in net unrealized appreciation/depreciation	151,007,102		32,543,124		(125,247,771)
Net realized and unrealized gain (loss)	225,050,768		(863,611,244)		(368,561,922)
Net income (loss)	218,419,388		(872,084,399)		(370,328,286)
ProShares Ultra Bloomberg Crude Oil [Member] | Futures Contracts [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	43,093,616		(297,227,106)		(109,160,069)
ProShares Ultra Bloomberg Crude Oil [Member] | Swap Agreements [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	30,967,424		(598,949,990)		(134,165,888)
Change in net unrealized appreciation/depreciation on
Unrealized gain (loss) on derivatives	127,535,160		4,004,508		(78,138,990)
ProShares Ultra Bloomberg Natural Gas [Member]
Investment Income
Interest	72,943		20,167		15,961
Expenses
Management fee	325,435		574,158		455,794
Brokerage commissions and fees	131,994		207,344		88,748
Total expenses	457,429		781,502		544,542
Net investment income (loss)	(384,486)		(761,335)		(528,581)
Net realized gain (loss) on
Short-term U.S. government and agency obligations	(698)		4,341		5,068
Net realized gain (loss)	17,571,111		(100,772,476)		(6,459,728)
Change in net unrealized appreciation/depreciation on
Futures contracts	(3,776,159)		41,202,162		(31,232,744)
Short-term U.S. government and agency obligations	(819)		(296)		(1,537)
Change in net unrealized appreciation/depreciation	(3,776,978)		41,201,866		(31,234,281)
Net realized and unrealized gain (loss)	13,794,133		(59,570,610)		(37,694,009)
Net income (loss)	13,409,647		(60,331,945)		(38,222,590)
ProShares Ultra Bloomberg Natural Gas [Member] | Futures Contracts [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	17,571,809		(100,776,817)		(6,464,796)
ProShares Ultra Gold [Member]
Investment Income
Interest	249,319		42,700		54,755
Expenses
Management fee	900,227		839,083		1,212,064
Brokerage commissions and fees	43		41		39
Total expenses	900,270		839,124		1,212,103
Net investment income (loss)	(650,951)		(796,424)		(1,157,348)
Net realized gain (loss) on
Short-term U.S. government and agency obligations	(806)		(393)		1,361
Net realized gain (loss)	5,815,759		(18,606,208)		(9,672,972)
Change in net unrealized appreciation/depreciation on
Futures contracts	(13,760)		(9,780)		19,140
Short-term U.S. government and agency obligations	(4,389)		2,086		5,375
Change in net unrealized appreciation/depreciation	(2,198,661)		(4,309,443)		8,888,643
Net realized and unrealized gain (loss)	3,617,098		(22,915,651)		(784,329)
Net income (loss)	2,966,147		(23,712,075)		(1,941,677)
ProShares Ultra Gold [Member] | Futures Contracts [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	29,500		(16,180)		(23,260)
ProShares Ultra Gold [Member] | Forward Agreements [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	5,787,065		(18,589,635)		(9,651,073)
Change in net unrealized appreciation/depreciation on
Unrealized gain (loss) on derivatives	(2,180,512)		(4,301,749)		8,864,128
ProShares Ultra Silver [Member]
Investment Income
Interest	842,215		156,353		179,642
Expenses
Management fee	3,021,562		2,664,160		4,148,207
Brokerage commissions and fees	45		52		43
Total expenses	3,021,607		2,664,212		4,148,250
Net investment income (loss)	(2,179,392)		(2,507,859)		(3,968,608)
Net realized gain (loss) on
Short-term U.S. government and agency obligations	145		(441)		8,226
Net realized gain (loss)	62,342,586		(78,309,750)		(155,543,194)
Change in net unrealized appreciation/depreciation on
Futures contracts	(18,330)		(7,470)		12,640
Short-term U.S. government and agency obligations	4,909		(9,125)		(11,363)
Change in net unrealized appreciation/depreciation	1,571,491		(10,182,576)		(9,900,963)
Net realized and unrealized gain (loss)	63,914,077		(88,492,326)		(165,444,157)
Net income (loss)	61,734,685		(91,000,185)		(169,412,765)
ProShares Ultra Silver [Member] | Futures Contracts [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	45,750		(19,600)		(52,451)
ProShares Ultra Silver [Member] | Forward Agreements [Member]
Net realized gain (loss) on
Gain (loss) on sale of derivatives	62,296,691		(78,289,709)		(155,498,969)
Change in net unrealized appreciation/depreciation on
Unrealized gain (loss) on derivatives	1,584,912		(10,165,981)		(9,902,240)
ProShares Ultra Euro [Member]
Investment Income
Interest	25,015		2,797		1,083
Expenses
Management fee	99,537		106,868		23,330
Total expenses	99,537		106,868		23,330
Net investment income (loss)	(74,522)		(104,071)		(22,247)
Net realized gain (loss) on
Foreign currency forward contracts	138,959		(1,982,208)		(420,533)
Short-term U.S. government and agency obligations	154		(109)		5
Net realized gain (loss)	139,113		(1,982,317)		(420,528)
Change in net unrealized appreciation/depreciation on
Foreign currency forward contracts	(1,178,930)		708,291		(204,333)
Short-term U.S. government and agency obligations	505		(369)		(182)
Change in net unrealized appreciation/depreciation	(1,178,425)		707,922		(204,515)
Net realized and unrealized gain (loss)	(1,039,312)		(1,274,395)		(625,043)
Net income (loss)	(1,113,834)		(1,378,466)		(647,290)
ProShares Ultra Yen [Member]
Investment Income
Interest	16,858		3,609		1,101
Expenses
Management fee	62,705		48,032		21,963
Total expenses	62,705		48,032		21,963
Net investment income (loss)	(45,847)		(44,423)		(20,862)
Net realized gain (loss) on
Foreign currency forward contracts	717,086		(472,913)		(540,398)
Short-term U.S. government and agency obligations	(34)		6		94
Net realized gain (loss)	717,052		(472,907)		(540,304)
Change in net unrealized appreciation/depreciation on
Foreign currency forward contracts	(603,387)		276,556		144,064
Short-term U.S. government and agency obligations	(510)		260		(289)
Change in net unrealized appreciation/depreciation	(603,897)		276,816		143,775
Net realized and unrealized gain (loss)	113,155		(196,091)		(396,529)
Net income (loss)	$ 67,308		$ (240,514)		$ (417,391)

[1] The operations include the activity of: ProShares Managed Futures Strategy through March 30, 2016, and ProShares UltraShort Bloomberg Commodity and ProShares Ultra Bloomberg Commodity through September 1, 2016, the date of liquidation, respectively. See Note 1.

[2] The operations include the activity of ProShares Ultra Australian Dollar through June 29, 2015, the date of liquidation, respectively. See Note 1.